CN106844844B

CN106844844B - Consider the three-dimensional season cracking model of bending contribution effect

Info

Publication number: CN106844844B
Application number: CN201611160380.0A
Authority: CN
Inventors: 黄书岭; 丁秀丽; 李欢; 邬爱清; 徐平; 付敬; 高源�; 朱良韬
Original assignee: Changjiang River Scientific Research Institute Changjiang Water Resources Commission
Current assignee: Changjiang River Scientific Research Institute Changjiang Water Resources Commission
Priority date: 2016-12-15
Filing date: 2016-12-15
Publication date: 2018-08-07
Anticipated expiration: 2036-12-15
Also published as: CN106844844A

Abstract

The invention discloses the three-dimensional season cracking model that effect is contributed in a kind of consideration bending, the three-dimensional season cracking model includes that the rock mass of consideration bending contribution effect carefully sees particle three-dimensional paralleling binding stress mode, considers that the rock mass of Torsion Coupling effect carefully sees particle three-dimensional paralleling binding timeliness deterioration damped expoential pattern formula, considers Torsion Coupling effect and mole coulomb with stretching cut-off limit carefully sees particles parallel and bonds season cracking criterion and consider the thin sight particle three-dimensional linear contact model of damping effect.The present invention is adapted under the conditions of three-dimensional stress space this kind of rock mass of the relationship index of coincidence type between stress and crack propagation velocity, can predict country rock long-time stability of this kind of deep rock mass engineering project under the conditions of triaxiality, evaluation and optimization design provide technical support.

Description

Consider the three-dimensional season cracking model of bending contribution effect

Technical field

The present invention relates to the three-dimensional thin sight season cracking analysis technical fields of engineering rock mass, and in particular to a kind of consideration bending tribute Offer the three-dimensional season cracking model of effect.

Background technology

Unstability and destruction after deep rock mass engineering project excavation are frequently not that immediately occurred after excavation, are usually present The hysteresis quality of apparent deformation fracture timeliness and catastrophe (rock burst, large deformation etc.), seriously endangers the construction safety and length of engineering Phase runs.Currently, the timeliness achievements in mechanical research in terms of thin sight is relatively fewer.《Buried griotte Fracture propagation time effect Particle flow simulation》One text has carried out experiment and two-dimensional numerical analysis (rock mechanics to the time effect of silk screen griotte rupture With engineering journal, 2011, Vol.30 No.10:1989-1996)；《Silk screen griotte creep impairment evolution mesomechanics feature Numerical simulation study》The one two-dimentional creep meso mechanical model of text application is short-term to silk screen griotte and long-term strength feature carries out Numerically modeling (rock-soil mechanics, 2013, Vol.34 No.12:3601-3608).This class model is expanded according to driving stress and crackle Relationship between exhibition speed is used for describing two-dimentional season cracking of the rock carefully in sight level, is suitable for stress and crackle under planar condition This kind of rock mass of index of coincidence expression way between expansion rate.This class model still has following shortcoming：(1) this class model Suitable for plane stress or plane strain problems, for must take into consideration the deep rock mass engineering project problem under the conditions of triaxiality, Such two dimensional model lacks adaptability due to cannot describe influence that triaxiality destroys rock mass secular distortion；(2) parallel viscous After knot fracture, the force of sliding friction in a direction is only considered between particle, does not account for being broken intergranular normal direction contact Force way, the thin motion mode for seeing particle under external load when not meeting three dimensions problem after rock masses fracturing and adjacent The mode of particle friction power interaction；(3) intergranular shear fracture criterion is one parallel with paralleling binding direct stress Horizontal linear namely this shear fracture criterion are unrelated with paralleling binding direct stress state, as long as paralleling binding shear stress is big In or equal to fix paralleling binding shear fracture intensity, shear fracture can occur between particle, can not embody different flat in rock mass Row, which bonds direct stress, has the objective fact of different paralleling binding shear fracture intensity；(4) for this friction caking property of rock mass Material, the paralleling binding model of this above-mentioned quasi-tradition do not account for the contribution effect for both bonding moment of flexure and bonding torque, do not have yet Have and considers that the difference of the two acts on the influence to rock mass pulling damage and failure by shear.

Invention content

The purpose of the present invention is in view of the above technical problems, provide a kind of three-dimensional season cracking of consideration bending contribution effect Model, the model are adapted under the conditions of three-dimensional stress space this of the relationship index of coincidence type between stress and crack propagation velocity Class rock mass can predict country rock long-time stability of this kind of deep rock mass engineering project under the conditions of triaxiality, evaluates and optimize Design provides technical support.

In order to achieve this, the three-dimensional season cracking model for considering bending contribution effect designed by the present invention, feature It is：The three-dimensional season cracking model includes considering that the rock mass of bending contribution effect carefully sees particle three-dimensional paralleling binding stress mould Formula considers that the rock mass of Torsion Coupling effect carefully sees particle three-dimensional paralleling binding timeliness deterioration damped expoential pattern formula, considers bending Coupling effect and mole coulomb limited with stretching cut-off carefully see particles parallel and bond season cracking criterion and consideration damping effect It is thin to see particle three-dimensional linear contact model.

In above-mentioned technical proposal, it is described consider bending contribution effect three-dimensional season cracking model be suitable for three dimensional particles from Dissipate element method, three dimensional particles discontinuous deformation analysis and three dimensional particles manifold element method.

In above-mentioned technical proposal, consider that torque carefully sees rock mass the percentage contribution of particle three-dimensional paralleling binding direct stress, institute It is that carefully to see particle three-dimensional parallel for rock mass that the rock mass of the considerations of stating bending contribution effect, which carefully sees particle three-dimensional paralleling binding stress mode, Bond direct stress calculation formulaIn be provided with the torque contribution factorConsider that moment of flexure carefully sees rock mass The percentage contribution of particle three-dimensional paralleling binding shear stress contributes the rock mass of effect carefully to see particle three-dimensional paralleling binding in consideration bending Rock mass in stress mode carefully sees particle three-dimensional paralleling binding Calculation Shear formulaIn be provided with it is curved Square contribution factorAbove-mentionedWithCalculation formula in,Particle three-dimensional paralleling binding radius is carefully seen for rock mass,For The torque contribution factor for determining percentage contribution of the torque in stress, To be used to determine moment of flexure in stress In percentage contribution moment of flexure contribution factor,I is the moment of inertia that rock mass carefully sees particle three-dimensional paralleling binding, and J is rock Body carefully sees the polar moment of inertia of particle three-dimensional paralleling binding, and A is that rock mass carefully sees particle three-dimensional paralleling binding area；For i-th of rock Body carefully sees the direct stress of particle three-dimensional paralleling binding,The shear stress of particle three-dimensional paralleling binding is carefully seen for i-th of rock mass,The rock mass of respectively i-th contact carefully see particle three-dimensional paralleling binding normal force, tangential resultant force, It is tangential to close torque and normal direction moment of flexure, wherein+=symbol is the reflexive operator of addition, wherein in formula,The displacement increment of particle three-dimensional paralleling binding normal direction is carefully seen for rock mass,Particle three-dimensional paralleling binding method is carefully seen for rock mass To rigidity, A is that rock mass carefully sees particle three-dimensional paralleling binding area,In formula,Respectively The tangential ss direction force of particle three-dimensional paralleling binding, tangential st direction force are carefully seen for rock mass, wherein ss and st is phase on same plane The code name of mutual vertical both direction；In formula,Respectively rock mass carefully sees particle The tangential directions the ss torque of three-dimensional paralleling binding, the tangential directions st torque；=symbol is subtraction from inverse operation It accords with, in formula,The relative rotation increment of particle three-dimensional paralleling binding normal direction is carefully seen for rock mass,Particle three is carefully seen for rock mass Tie up paralleling binding shear stiffness.

It is described to consider that the rock mass of Torsion Coupling effect carefully sees the deterioration of particle three-dimensional paralleling binding timeliness in above-mentioned technical proposal Damped expoential pattern formula, be included in rock mass carefully see particles parallel bond timeliness deterioration decaying when, be provided with exponential type with consideration it is curved The relevant rock mass of paralleling binding stress for turning round contribution factor carefully sees particle three-dimensional paralleling binding deterioration evanescent mode, sees exponential type more New rateIn formula,To judge that it is flat that rock mass carefully sees particle three-dimensional Row bonds stress threshold values when starting timeliness deterioration decaying,Particle three-dimensional paralleling binding tensile strength is carefully seen for rock mass, To consider the three-dimensional paralleling binding stress ratio of bending contribution factor, β₁It is thin inside the rock mass of index overall variation in order to control to see particle Three-dimensional paralleling binding timeliness deterioration factor, β₂Thin sight particle three-dimensional is parallel viscous inside the rock mass of index subscript part variation in order to control Timeliness deterioration factor is tied,Particle three-dimensional paralleling binding stress is carefully seen for rock mass, e is the truth of a matter of natural logrithm；

In considering that the rock mass of Torsion Coupling effect carefully sees particle three-dimensional paralleling binding timeliness deterioration damped expoential pattern formula Provided with three-dimensional paralleling binding diameter at any time gradually deterioration decaying and with consider bending contribution factor paralleling binding stress Relevant exponential type pattern is shown in three-dimensional paralleling binding diameter formulaIn formula,Particle three-dimensional is carefully seen for rock mass Paralleling binding deteriorates the diameter of decaying at any time,Diameter when particle three-dimensional paralleling binding is not decayed is carefully seen for rock mass, Δ t is Rock mass carefully sees the incremental time of particle three-dimensional paralleling binding timeliness decaying deterioration；

Consider that the rock mass of Torsion Coupling effect is carefully seen in particle three-dimensional paralleling binding timeliness deterioration damped expoential pattern formula to set The timeliness deterioration evanescent mode that rock mass carefully sees particle three-dimensional paralleling binding area, the moment of inertia and polar moment of inertia has been set, has been seen respectively viscous Tie three-dimensional paralleling binding areal calculation formula when unit thickness is 1Bond three-dimensional when unit thickness is 1 Paralleling binding the moment of inertia calculation formulaBond three-dimensional paralleling binding polar moment of inertia meter when unit thickness is 1 Calculate formulaWherein, β is the timeliness decay factor that rock mass carefully sees particle three-dimensional paralleling binding diameter, meter Formula is calculated to seeIts In,A'、I'、J’、Be expressed as rock mass carefully see particle three-dimensional paralleling binding deteriorate at any time decaying bonding it is straight Diameter bonds radius, bond area, bonds the moment of inertia, bonds polar moment of inertia and diameter multiplier,A、I、J、 Bonding diameter when particle three-dimensional paralleling binding is not decayed is carefully seen for rock mass, is bonded radius, bond area, is bonded the moment of inertia, is viscous It ties polar moment of inertia and bonds diameter multiplier, while rock mass carefully sight is obtained according to this three-dimensional exponential type timeliness deterioration evanescent mode The initial time step-length of grain paralleling binding rupture, is shown in formulaWherein, The rock mass contacted for i-th carefully sees particle three-dimensional paralleling binding diameter multiplier, n_cIt is parallel that particle three-dimensional is carefully seen for first rock mass Bond the number of the cycle calculations needed for rupture, β_σ、β_τRespectively rock mass is carefully seen under particle three-dimensional paralleling binding tensile strength state The timeliness deterioration factor and three-dimensional paralleling binding shear strength state under timeliness deteriorate the factor, e is the truth of a matter of natural logrithm, ∞ For infinity；Rock mass carefully sees the deterioration factor-beta of the timeliness under particle three-dimensional paralleling binding tensile strength state_σParticle is carefully seen with rock mass Timeliness under three-dimensional paralleling binding shear strength state deteriorates factor-beta_τIt can be respectively by formula：With The two equations are solved according to iterative method (Newton iteration method or Stefansson Accelerated iteration method) or second-class method to obtain, whereinParticle three-dimensional paralleling binding knot tensile strength is carefully seen for rock mass,The cohesive strength of particle three-dimensional paralleling binding is carefully seen for rock mass,The internal friction angle of particle three-dimensional paralleling binding, F are carefully seen for rock mass_σFor β_σFunction, F_τFor β_τFunction, π is pi.

In above-mentioned technical proposal, the consideration Torsion Coupling effect and with stretch cut-off limit a mole coulomb carefully see particle Paralleling binding season cracking criterion refers to when judging that rock mass carefully sees particle three-dimensional paralleling binding season cracking, using embedded Consider bending contribution effect and end mole coulomb season cracking criterion of limit with stretching to judge, sees formulaWherein, f^sIt is thin for mole-coulomb It sees particle three-dimensional and bonds shearing season cracking criterion, fⁿParticle three-dimensional is carefully seen for mole-coulomb bonds stretching season cracking criterion,Respectively rock mass carefully sees particle three-dimensional paralleling binding tensile strength, shearing strength,It is to refer to containing for i-th of contact The rock mass of number type time effect and consideration moment of flexure contribution factor carefully sees particle three-dimensional paralleling binding direct stress, and calculation formula is For i-th contact time effect containing exponential type and consideration torque contribution because The rock mass of son carefully sees particle three-dimensional paralleling binding shear stress, and calculation formula isIn the standard Contain exponential type time effect in three-dimensional paralleling binding stress then, see rock mass carefully see particle three-dimensional paralleling binding diameter when Imitate decay factor calculation formulaf^sMore than or equal to 0 table Show that rock mass carefully sees particle three-dimensional paralleling binding shear fracture, f^sParticle three-dimensional paralleling binding is carefully seen less than 0 expression rock mass not occur Shear fracture；fⁿParticle three-dimensional paralleling binding tensile fracture, f are carefully seen more than or equal to 0 expression rock massⁿRock mass carefully sight is indicated less than 0 Tensile fracture does not occur for the three-dimensional paralleling binding of grain.

In above-mentioned technical proposal, it refers to rock mass that the rock mass of the consideration damping effect, which carefully sees particle three-dimensional linear contact model, After season cracking, pass through Three-Dimensional contact reference distance g_rIt sets thin particle space of seeing inside rock mass and contacts distance, consider resistance It is that thin particle space of seeing is contacted away from calculation formula inside rock mass that the rock mass of Buddhist nun's effect, which carefully sees particle three-dimensional linear contact model,Wherein,For contact jaw a Coordinate,For the coordinate of contact jaw b, R^a、R^bRespectively inside rock mass the thin particle radius for seeing contact jaw a and The particle radius of contact jaw b；

Consider to see particle sky provided with thin inside consideration rock mass in the thin sight particle three-dimensional linear contact model of damping effect Between the linear contact mode that deforms, carefully seen inside rock mass and be provided with the coupling for considering three-dimensional sliding friction surface power between particle Binding mode is closed, the thin linear Three-Dimensional contact normal direction linear force calculation formula for seeing particle space deformation is inside rock massTake M_l=1 is relative vector accumulation mode, takes M_l=0 is tired for absolute vectors Add pattern, the tangential linear force calculation formula of linear contact that particle space deformation is carefully seen inside rock mass isWithWherein,k_n、k_sThe linear contact of particle space deformation is carefully seen for rock mass inside Normal direction, tangential linear rigidity, Δ δ_nFor rock mass internal particle linear contact Normal Displacement increment,For rock The initial normal force increment size and tangential force increment size of internal portion particle three-dimensional linear contact,Exist for tangential linear force Thin see carefully sees the tangential side st of particle three-dimensional linear contact inside the tangential directions ss of particle three-dimensional linear contact and rock mass inside rock mass To component, ss and st are the code name of orthogonal both direction on same plane,For particle force of sliding friction, pass through Friction coefficient μ withProduct obtains,Stiction when not slided for particle, Δ δ_st、Δδ_ssIt is thin respectively inside rock mass to see It is thin inside the displacement increment and rock mass in the tangential directions ss of particle three-dimensional linear contact to see the tangential directions st of particle three-dimensional linear contact Displacement increment；

Consider that the thin of damping effect sees the space damping mould that Three-Dimensional contact is arranged in particle three-dimensional linear contact model simultaneously The damping of formula, wherein normal direction uses full normal mode M_d={ 0,2 } and tensionless winkler foundation pattern M_dTwo kinds of={ 1,3 }, passes through formulaIt calculates, wherein F^*For the contact of rock mass internal particle linear Full normal direction damping force, expression formula are The linear of particle space deformation is carefully seen for rock mass inside Contact normal direction linear force, m_cFor equivalent particle quality, by formulaIt calculates；

Tangential damping uses full shear mode M_d={ 0,1 } and sliding and shear mode M_d={ 2,3 }, according to formulaAnd formulaIt is calculated, Wherein,The rate in the tangential directions ss is contacted for linear, ss is the directions ss in linear contact local coordinate system,The rate in the tangential directions st is contacted for linear, st is the directions st in linear contact local coordinate system, the directions st It is mutually perpendicular to the directions ss,For the normal direction damping force of rock mass internal particle linear contact, β_nFor rock mass internal particle three Normal direction damped coefficient, the β of dimensional linear contact_sFor the tangential damped coefficient of rock mass internal particle linear contact, k_nFor in rock mass Normal direction linear rigidity, the k of portion's particle three-dimensional linear contact_sFor rock mass internal particle linear contact tangential linear rigidity,For rock mass internal particle linear contact normal direction rate,ForWithConjunction rate, referred to as linear connects Tactile tangential velocity, the relationship between three are：m_cFor equivalent particle quality, m⁽¹⁾For rock mass inside The granular mass for the first contact jaw that particle is contacted with particle, m⁽²⁾The second contact jaw contacted with particle for rock mass internal particle Granular mass, F^dFor total damping power,For linear contact normal direction damping force,For the tangential of linear contact Damping force, F^dFor Resultant force, referred to as linear contacts total damping power, and triadic relation is： The tangential directions ss of particle three-dimensional linear contact are carefully seen inside rock mass tangentially to damp With the thin component for seeing the tangential directions st of particle three-dimensional linear contact inside rock mass.

Advantage and advantage of the present invention is mainly reflected in：

(1) model structure in the present invention includes considering the thin sight particle three-dimensional paralleling binding stress mould of bending contribution effect Formula, considers Torsion Coupling at the thin sight particle three-dimensional paralleling binding timeliness deterioration damped expoential pattern formula for considering Torsion Coupling effect Effect and the thin sight for bonding season cracking criterion with the thin sight particles parallel of mole-coulomb for stretching cut-off limit, considering damping effect Particle three-dimensional linear contact model etc., this four part constitutes complete model structure system, while giving the model construction Method and specific implementation flow, convenient for carrying out Numerical Implementation on numerical value platform in three-dimensional thin see.

(2) it is provided in the model constructed by the present invention and considers that the thin sight particle three-dimensional paralleling binding of bending contribution effect is answered Force mode is not only carefully seen during particles parallel bonds normal stress three-dimensional computations formula in rock mass and is provided with moment of flexure contribution factor, and And the torque contribution factor is provided in paralleling binding tangential stress three-dimensional computations formula.This model structure and construction method, Not only allow for the percentage contribution that moment of flexure bonds direct stress to carefully seeing particles parallel, it is contemplated that torque is tangentially cut paralleling binding and answered The percentage contribution of power, and influence of the percentage contribution of moment of flexure and torque to rock mass long-term strength is also contemplated, it is suitble to description one The mesomechanics of class rock mass rupture three dimensions problem, while reducing thin see during particles parallel bonds season cracking and generating Strong energy impact wave secondary damage caused by adjacent domain.

(3) it is constructed in the present invention and considers that the thin sight particle three-dimensional paralleling binding timeliness deterioration decaying of Torsion Coupling effect refers to Number pattern formula is provided with exponential type and considers bending contribution when being included in rock mass and carefully seeing particles parallel and bond timeliness deterioration decaying The relevant thin sight particle three-dimensional paralleling binding of paralleling binding stress of the factor deteriorates evanescent mode, and it is straight to be provided with three-dimensional paralleling binding The diameter relevant exponential type pattern of paralleling binding stress with consideration bending contribution factor that gradually deterioration decays at any time, is provided with The timeliness such as three-dimensional paralleling binding area, the moment of inertia and polar moment of inertia deteriorate evanescent mode；It is bad according to this three-dimensional exponential type timeliness Change evanescent mode estimation rock mass and carefully sees the initial time step-length that particles parallel bonds rupture.This three-dimensional exponential type forming types are suitable Close the three-dimensional mesomechanics season cracking mechanism and response pattern of a kind of deep rock mass under description spatiality.

(4) embedded to consider Torsion Coupling effect and band in the present invention in the constructed thin sight season cracking model of three-dimensional The thin particles parallel of seeing of mole-coulomb for stretching cut-off limit bonds season cracking criterion.Particles parallel, which is carefully seen, in rock mass bonds timeliness When rupture, consider Torsion Coupling effect and carefully see particles parallel with mole-coulomb for stretching cut-off limit to bond using embedded Season cracking criterion judges；Exponential type time effect is contained in the paralleling binding stress of the criterion, and in paralleling binding It is provided with moment of flexure contribution factor in direct stress, the torque contribution factor is provided in paralleling binding shear stress.This model structure In carefully see particles parallel bond season cracking criterion construction method, timeliness related to paralleling binding direct stress can not only be described The difference of shear fracture intensity can also reasonably be expressed carefully seeing timeliness tensile fracture, and consider moment of flexure and torque Influence of the percentage contribution to paralleling binding season cracking meets a kind of Three-dimensional Rock under spatiality and carefully sees season cracking pattern.

(5) present invention is in the constructed thin sight season cracking model of three-dimensional, the embedded thin sight particle for considering damping effect Linear contact model structure sets thin sight particle three-dimensional after rock mass season cracking by Three-Dimensional contact reference distance Space contacts distance, is provided with and considers the thin Three-Dimensional contact pattern for seeing particle space Three-direction deformation, is provided with examines between particles Consider the three dimensions coupling pattern of three-dimensional sliding friction surface power, while the three dimensions damping mode of four kinds of contacts be set, Particle space movement and stress characteristic of a kind of deep engineering rock mass after season cracking under three-dimensional stress constraint can be described rationally.

Description of the drawings

Fig. 1 is carefully to see particle in model of the present invention to contact schematic diagram with particle.

Fig. 2 is carefully to see particle in model of the present invention to contact schematic diagram with rigid wall.

Fig. 3 is carefully to see particle space overlap condition schematic diagram in model of the present invention.

Fig. 4 is carefully to see particle Rigidity Calculation schematic three dimensional views in model of the present invention.

Fig. 5 is carefully to see particle in model of the present invention to bond linear tangential force and tangential displacement schematic diagram

Fig. 6 is carefully to see particles stick in model of the present invention to touch this structure physical model schematic diagram.

Fig. 7 is carefully to see particle linear parallel in invention model to bond three dimensional structure diagram.

Fig. 8 is to consider that bending contributes effect and carefully sees particle with mole coulomb for stretching cut-off limit in model of the present invention to bond Season cracking criterion schematic diagram.

Particle is carefully seen in the model of the present invention of the positions Fig. 9 bonds diameter (or radius) timeliness deterioration decaying schematic diagram.

Figure 10 is model three-dimensional paralleling binding diameter (or radius) logarithm turnover rate of the present invention and stress curve schematic diagram.

Figure 11 is the power and moment distribution amount schematic diagram that particle three-dimensional contact surface is carefully seen in model of the present invention.

Figure 12 is the normal direction that particle three-dimensional contact surface is carefully seen in model of the present invention and tangential vectorial schematic diagram.

Figure 13 is model construction flow diagram of the present invention.

Figure 14 is model assay maps of the present invention.

Figure 15 is model creeping displacement of the present invention and time history.

Figure 16 is the creeping displacement and time history under model difference bending of the present invention contribution effect.

Wherein：The centre distance d of 1-two particles, 2-rock mass carefully see intergranular half contact distance, the carefully sight of 3-rock mass Half reference distance g of intergranular_r, 4-rock mass carefully see the coordinate of particle a, and 5-rock mass carefully see the coordinate of particle b, and 6-rock mass are carefully seen Particle surface contacts the centre coordinate of distance, and 7-rock mass carefully see particle surface contact distance g_s, 8-rock mass are carefully seen intergranular Contact unit normal vector, 9-rock mass carefully see the radius R of particle a^a, 10-rock mass carefully see the radius R of particle b^b, 11-rock mass carefully see The contact lap U of grain contact point, 12-represent b (rock mass carefully sees particle or boundary wall) rigidity (normal direction, it is tangential just Degree is referred to as) k^b, 13-represent rigidity (normal direction, shear stiffness are referred to as) k of a (rock mass carefully sees particle or boundary wall)^a, 14- generations The equivalent stiffness of table contact point, 15- represent total displacement increment Delta U_i, 16- represents initial normal forceIncrement size, 17- are represented It initially contacts force vector and 18- represents initial tangential forceIncrement size, 19- represent the thin sight season cracking of constructed three-dimensional Model normal direction displacement increment Δ δ_n, the constructed three-dimensional of 20- representatives is thin to see season cracking model tangential displacement increment Delta δ_s, 21- generations Table carefully sees particles parallel and bonds tensile strength values22- represents thin particles parallel of seeing and bonds normal stiffness23- represents thin See the normal stiffness K of grain contact point_n, 24-, which is represented, carefully sees particles parallel bonding shear stiffness25- represents thin particle of seeing and puts down Row bond shear strength, 25.1- are representedCarefully to see the cohesive strength intensity of particles parallel bonding, 25.2- represents thin particle of seeing and puts down The internal friction angle of row bonding26 represent the thin shear stiffness K for seeing grain contact point_s, 27- represents rock mass and carefully sees particle three-dimensional line Property contact slide friction coefficient, 28- are represented as rock mass and carefully see particle three-dimensional linear contact normal direction damped coefficient β_n, 29- represents rock Body carefully sees the tangential damped coefficient β of particle three-dimensional linear contact_s, 30- is represented as rock mass and carefully sees particles parallel bonding diameter (or half Diameter) multiplier31- represents rock mass and carefully sees particles parallel bonding diameter32-, which is represented, considers bending contribution effect and with stretching End limit mole-coulomb season cracking criterion, 33-i-th contact comprising exponential time effect and consider torque contribution because The rock mass of son carefully sees particles parallel and bonds shear stress34-i-th contact includes exponential time effect and consideration moment of flexure The rock mass of contribution factor carefully sees particles parallel and bonds direct stress35- represents rock mass and carefully sees particles parallel bonding timeliness decaying Radius36- represents rock mass and carefully sees the diameter that particles parallel bonds timeliness decaying37- represents rock mass and carefully sees particles parallel Bond diameter when not decaying38-, which represents rock mass and carefully sees particles parallel, bonds radius when not decaying39- is represented as pair Number turnover rate ln (γ), 40- represent stress threshold values when rock mass carefully sees particles parallel bonding beginning timeliness deterioration decaying41- It represents thin particles parallel of seeing and bonds tensile strength42- represents the paralleling binding stress ratio for considering moment of flexure contribution factor 43- represents thin sight particle three-dimensional paralleling binding timeliness deterioration factor β inside the rock mass of control characteristic subscript part variation₂, 44- generations Table carefully sees particles parallel and bonds moment of flexure direction vector, and 45- represents thin particles parallel of seeing and bonds torque direction vector, and 46- represents thin The force vector that particles parallel bonds tangential direction is seen, 47- represents the thin force vector seen particles parallel and bond normal orientation, 48- generations Table carefully sees particles parallel and bonds diameter, and 49- is represented and carefully seen particles parallel bonding unit thickness, and general value is that 1,50- is represented carefully The component that particles parallel bonds the tangential directions ss is seen, 51- represents the thin component seen particles parallel and bond the tangential directions st, 52- generations Table carefully sees the normal vector n of particle contact surface_n, 53-, which is represented, carefully sees particles parallel bonded contact face.

Specific implementation mode

Below in conjunction with the drawings and specific embodiments, the present invention is described in further detail：

A kind of three-dimensional season cracking model of consideration bending contribution effect designed by the present invention, the three-dimensional season cracking Model includes considering that the rock mass of bending contribution effect carefully sees particle three-dimensional paralleling binding stress mode, considers Torsion Coupling effect Rock mass carefully sees particle three-dimensional paralleling binding timeliness deterioration damped expoential pattern formula, considers Torsion Coupling effect and limited with cut-off is stretched Mole coulomb carefully see particles parallel bond season cracking criterion and consider damping effect thin sight particle three-dimensional linear contact mould Type.

In above-mentioned technical proposal, consider that torque carefully sees rock mass the percentage contribution of particle three-dimensional paralleling binding direct stress, institute It is that carefully to see particle three-dimensional parallel for rock mass that the rock mass of the considerations of stating bending contribution effect, which carefully sees particle three-dimensional paralleling binding stress mode, Bond direct stress calculation formulaIn be provided with the torque contribution factor

Consider that moment of flexure carefully sees rock mass the percentage contribution of particle three-dimensional paralleling binding shear stress, is considering bending contribution effect Rock mass carefully see the rock mass in particle three-dimensional paralleling binding stress mode and carefully see particle three-dimensional paralleling binding Calculation Shear formulaIn be provided with moment of flexure contribution factor

Above-mentionedWithCalculation formula in,Particle three-dimensional paralleling binding radius is carefully seen for rock mass,To be used for really Determine the torque contribution factor of percentage contribution of the torque in stress, For for determining tribute of the moment of flexure in stress The moment of flexure contribution factor of degree is offered,I is the moment of inertia that rock mass carefully sees particle three-dimensional paralleling binding, and J is that rock mass is carefully seen The polar moment of inertia of particle three-dimensional paralleling binding, A are that rock mass carefully sees particle three-dimensional paralleling binding area；

The direct stress of particle three-dimensional paralleling binding is carefully seen for i-th of rock mass,It is flat that particle three-dimensional is carefully seen for i-th of rock mass The shear stress of row bonding,The rock mass of respectively i-th contact carefully sees particle three-dimensional paralleling binding method Xiang Li, tangential resultant force, tangential conjunction torque and normal direction moment of flexure, wherein+=symbol is addition from inverse operation Symbol, wherein in formula,The displacement increment of particle three-dimensional paralleling binding normal direction is carefully seen for rock mass,Particle three is carefully seen for rock mass Paralleling binding normal stiffness is tieed up, A is that rock mass carefully sees particle three-dimensional paralleling binding area,In formula,Respectively rock mass carefully sees the tangential ss direction force of particle three-dimensional paralleling binding, tangential st direction force, wherein ss and st For the code name of orthogonal both direction on same plane；In formula,Respectively The tangential directions the ss torque of particle three-dimensional paralleling binding, the tangential directions st torque are carefully seen for rock mass；=symbol For the reflexive operator of subtraction, in formula,The relative rotation increment of particle three-dimensional paralleling binding normal direction is carefully seen for rock mass,For Rock mass carefully sees particle three-dimensional paralleling binding shear stiffness.

In above-mentioned technical proposal, the consideration Torsion Coupling effect and with stretch cut-off limit a mole coulomb carefully see particle Paralleling binding season cracking criterion refers to when judging that rock mass carefully sees particle three-dimensional paralleling binding season cracking, using embedded Consider bending contribution effect and end mole coulomb season cracking criterion of limit with stretching to judge, sees formula

Wherein, f^sParticle three-dimensional is carefully seen for mole-coulomb bonds shearing season cracking criterion, fⁿFor mole-coulomb carefully sight Three-dimensional bond of grain stretches season cracking criterion,Respectively rock mass is carefully seen particle three-dimensional paralleling binding tensile strength, is resisted Intensity is cut,The rock mass of the time effect containing exponential type and consideration moment of flexure contribution factor that are contacted for i-th carefully sees particle three-dimensional Paralleling binding direct stress, calculation formula are Contain index for i-th of contact The rock mass of type time effect and the consideration torque contribution factor carefully sees particle three-dimensional paralleling binding shear stress, and calculation formula isExponential type time effect is contained in the three-dimensional paralleling binding stress of the criterion, See that rock mass carefully sees the timeliness decay factor calculation formula of particle three-dimensional paralleling binding diameterf^sParticle three-dimensional is carefully seen more than or equal to 0 expression rock mass Paralleling binding shear fracture, f^sParticle three-dimensional paralleling binding is carefully seen less than 0 expression rock mass, and shear fracture does not occur；fⁿMore than or equal to 0 Indicate that rock mass carefully sees particle three-dimensional paralleling binding tensile fracture, fⁿParticle three-dimensional paralleling binding is carefully seen less than 0 expression rock mass not send out Raw tensile fracture.

Tangential damping uses full shear mode M_d={ 0,1 } and sliding and shear mode M_d={ 2,3 }, according to formulaAnd formulaIt is calculated, In,The rate in the tangential directions ss is contacted for linear, ss is the directions ss in linear contact local coordinate system, Contact the rate in the tangential directions st for linear, st is that linear contacts directions st in local coordinate system, the directions st with The directions ss are mutually perpendicular to,For the normal direction damping force of rock mass internal particle linear contact, β_nIt is three-dimensional for rock mass internal particle Normal direction damped coefficient, the β of linear contact_sFor the tangential damped coefficient of rock mass internal particle linear contact, k_nFor rock mass inside Normal direction linear rigidity, the k of particle three-dimensional linear contact_sFor rock mass internal particle linear contact tangential linear rigidity, For rock mass internal particle linear contact normal direction rate,ForWithConjunction rate, referred to as linear contact Tangential velocity, the relationship between three is：m_cFor equivalent particle quality, m⁽¹⁾For rock mass inside The granular mass for the first contact jaw that grain is contacted with particle, m⁽²⁾The second contact jaw contacted with particle for rock mass internal particle Granular mass, F^dFor total damping power,For linear contact normal direction damping force,For the tangential resistance of linear contact Buddhist nun's power, F^dFor Resultant force, referred to as linear contacts total damping power, and triadic relation is： The tangential directions ss of particle three-dimensional linear contact are carefully seen inside rock mass tangentially to damp With the thin component for seeing the tangential directions st of particle three-dimensional linear contact inside rock mass.

A kind of construction method of the three-dimensional season cracking model of above-mentioned consideration bending contribution effect, it includes the following steps：

Step 1：The geometric parameters quantity that setting rock mass carefully sees the contact of particle three-dimensional paralleling binding includes paralleling binding area, puts down Row bonds the moment of inertia and paralleling binding polar moment of inertia, R^(a),R^(b)The particle radius at both ends is contacted for three-dimensional paralleling binding, is considered viscous Tie the area of three-dimensional paralleling binding of unit thickness when being 1, bond three-dimensional paralleling binding when unit thickness is 1 the moment of inertia and The polar moment of inertia of three-dimensional paralleling binding when unit thickness is 1 is bonded respectively by formula (2), formula (3), formula (4) come really It is fixed：

Wherein：Particle three-dimensional paralleling binding radius is carefully seen for rock mass,Particle three-dimensional paralleling binding diameter is carefully seen for rock mass Multiplier, A are that rock mass carefully sees particle three-dimensional paralleling binding area, and I is that rock mass carefully sees particle three-dimensional paralleling binding the moment of inertia, and J is thin See particle three-dimensional paralleling binding polar moment of inertia；

Step 2：The initial time step size increments Δ that the parallel grain of particle three-dimensional bonds timeliness decaying deterioration is carefully seen using rock mass T, calculates rock mass by three-dimensional exponential type function and carefully sees particles parallel and bond diameter, and formula (5) determines；

Wherein：To judge that three-dimensional rock mass carefully sees stress threshold values when particle starts timeliness deterioration decaying,For three-dimensional rock Body carefully sees particles parallel and bonds tensile strength,It is bonded to consider that the three-dimensional rock mass of the torque contribution factor carefully sees particles parallel Stress ratio,Particle three-dimensional paralleling binding stress, β are carefully seen for rock mass₁It is thin inside the rock mass of index overall variation in order to control to see particle Three-dimensional paralleling binding timeliness deterioration factor, β₂Thin sight particle three-dimensional is parallel viscous inside the rock mass of index subscript part variation in order to control Timeliness deterioration factor is tied,The diameter that particle three-dimensional paralleling binding deteriorates decaying at any time is carefully seen for three-dimensional rock mass,For three-dimensional Rock mass carefully sees diameter when particle three-dimensional paralleling binding is not decayed；

Step 3：According to the formula (5) in step 2, when the three-dimensional rock mass of setting carefully sees the exponential type of particles parallel bonding diameter Decay factor is imitated, sees formula (6)：

Wherein：β is the timeliness decay factor that rock mass carefully sees particle three-dimensional paralleling binding diameter,The diameter, radius and diameter multiplier for deteriorating decaying at any time for three-dimensional paralleling binding (refer to putting down Row bonds diameter and bonds the ratio of both ends smallest particles diameter), It is straight when not decaying for three-dimensional paralleling binding Diameter, radius, diameter multiplier；

Step 4：According to the formula (6) in the formula (1) in step 1~formula (4) and step 3,

Setting rock mass carefully sees particle three-dimensional paralleling binding geometric parameter timeliness deterioration evanescent mode.Under three-dimensional situation, rock Body carefully sees particle three-dimensional paralleling binding diameter and constantly deteriorates decaying as the time increases, area, the inertia of three-dimensional paralleling binding Square and polar moment of inertia increase also with the time and constantly deteriorate decaying, see formula (7), formula (8) and formula (9) respectively.

Wherein：A, I, J are respectively that rock mass carefully sees area, the moment of inertia, pole inertia when particle three-dimensional paralleling binding is not decayed Square,A', I', J' be expressed as rock mass carefully see the parallel grain of particle three-dimensional bond the radius for deteriorating decaying at any time, area, The moment of inertia, polar moment of inertia；

Step 5：The rock mass for calculating j-th to k-th successively carefully sees the three-dimensional paralleling binding method that particle includes time effect To torque (moment of flexure) increment and tangential torque (torque) increment, under three-dimensional situation, by the speed of paralleling binding both ends particle, angle Speed and given cycle calculations step Δ t_c, by following formula (10), formula (11), formula (12) and formula (13), determine Paralleling binding normal direction incremental displacementThe incremental displacement in the tangential directions st of paralleling bindingThe tangential side ss of paralleling binding To incremental displacementDetermine paralleling binding normal direction relative rotationThe relative rotation in the tangential directions ss of paralleling bindingThe relative rotation in the tangential directions st of paralleling bindingSs and st is orthogonal both direction on same plane Code name, in conjunction with the formula (6) in the formula (8) and formula (9) and step 3 in step 4, it may be determined that paralleling binding is tangential The torque increase in the directions st, the torque increase in the tangential directions ss and paralleling binding normal direction moment of flexure increment, are shown in formula (14), formula (15) and formula (16)；

Wherein：Ff, j, k are natural numbers, and 2≤j≤ff≤k, j are the rock mass for including time effect in each cycle calculations Thin particles parallel of seeing bonds uncracked initial index value after decaying, and ff is some intermediate index value, and k is each cycle calculations In comprising time effect rock mass carefully see particles parallel bond decaying after uncracked most end index value,Respectively I-th of rock mass carefully sees the absolute movement speed at the ends a and the ends b of particle contact,Respectively i-th of rock mass carefully sees particle The angular speed at the ends a and the ends b of contact, n_n、n_ss、n_stRespectively carefully see the normal direction unit vector of particle contact surface, the tangential directions ss Unit vector, the tangential directions st unit vector,It respectively carefully sees particles parallel and bonds normal direction Displacement increment, the displacement increment in the tangential directions ss, the tangential directions st displacement increment, I, J are respectively that rock mass carefully sees particle three The moment of inertia, polar moment of inertia when dimension paralleling binding is not decayed,For paralleling binding normal stiffness,For paralleling binding shear stiffness,Respectively the torque increase value in the tangential directions ss of paralleling binding, the torque increase value in the tangential directions st, For paralleling binding normal direction moment of flexure increment size, moment of flexure and torque press right-hand rule, determine that its direction vector, β are that rock mass is carefully seen The timeliness decay factor of particle three-dimensional paralleling binding diameter, Δ t_cIt is walked for the cycle calculations of paralleling binding both ends particle；

Step 6：According to the formula (10) in the formula (7) in step 4~formula (9), step 5~formula (13) and step Formula (6) in rapid 3, successively update calculate j-th to k-th rock mass and carefully see the three-dimensional that particle does not rupture and include time effect Paralleling binding normal force, tangential force, normal direction moment of flexure, tangential torque pass through following formula (17), formula (20), formula (23), public affairs Formula (24) calculate i-th of rock mass carefully see particle contact paralleling binding normal force, tangential force, normal direction moment of flexure, tangential torque；

I-th of rock mass carefully sees the paralleling binding normal force that particle contacts：

I-th of rock mass carefully sees the tangential ss direction force of paralleling binding that particle contacts：

I-th of rock mass carefully sees the tangential st direction force of paralleling binding that particle contacts：

I-th of rock mass carefully sees the paralleling binding that particle contacts：

I-th of rock mass carefully sees the tangential directions the ss torque of paralleling binding that particle contacts：

I-th of rock mass carefully sees the tangential directions the st torque of paralleling binding that particle contacts：

I-th of rock mass carefully sees the paralleling binding normal direction moment of flexure that particle contacts：

The paralleling binding that i-th of rock mass carefully sees particle contact tangentially closes torque and is：

Wherein：Respectively i-th A thin three-dimensional paralleling binding normal force for seeing particle contact, tangential ss direction force, tangential st direction force, three-dimensional paralleling binding normal direction Moment of flexure and the tangential directions the ss torque of paralleling binding, the tangential directions st torque, three-dimensional paralleling binding Normal Displacement increment, the tangential side ss To displacement increment, the tangential directions st displacement increment, +=is the reflexive operator of addition, and -=is the reflexive operator of subtraction,It is flat Row bonds normal stiffness,For paralleling binding shear stiffness, β is the timeliness decaying that rock mass carefully sees particle three-dimensional paralleling binding diameter The factor, A, I, J are respectively that rock mass carefully sees area, the moment of inertia, polar moment of inertia when particle three-dimensional paralleling binding is not decayed,For Paralleling binding normal direction relative rotation,For the tangential directions ss of paralleling binding relative rotation,For the tangential st of paralleling binding The relative rotation in direction, ff are that the rock mass comprising time effect is not broken after carefully seeing particles parallel bonding decaying in each cycle calculations The label split；

Step 7：Consider that torque carefully sees rock mass the percentage contribution of particle three-dimensional paralleling binding direct stress, three-dimensional parallel viscous It ties and the torque contribution factor is set in direct stress calculation formula It is parallel to consider that moment of flexure carefully sees rock mass particle three-dimensional Moment of flexure contribution factor is arranged in three-dimensional paralleling binding Calculation Shear formula in the percentage contribution for bonding shear stressAccording to three-dimensional paralleling binding direct stress formulaWith three-dimensional paralleling binding shear stress FormulaSimultaneously by A, I, J in the two formula andWith A', I', J' andIt replaces, then will Formula (6) in formula (7)~formula (9) and step 3 in step 4 substitutes into, can get comprising exponential type time effect and Consider the three-dimensional paralleling binding mormal stress of bending contribution effect and three-dimensional paralleling binding Calculation Shear formula, sees public affairs respectively Formula (25) and formula (26)；

Step 8：It will include exponential type time effect in step 7 and consider that effect is contributed in bendingIt substitutes into public Formula (27), it may be determined that comprising exponential type time effect and bending contribution effect and with mole coulomb paralleling binding for stretching cut-off limit Season cracking criterion (stretches broken for judging that rock mass carefully sees particle three-dimensional paralleling binding and whether ruptures and determine fracture mode Split pattern or shear fracture pattern), when the rock mass of the criterion is carefully seen and contains exponential type in particle three-dimensional paralleling binding stress Between effect and bending contribute effect；

Wherein：f^sParticle three-dimensional is carefully seen for mole-coulomb bonds shearing season cracking criterion, fⁿFor mole-coulomb carefully sight Three-dimensional bond of grain stretches season cracking criterion,For i-th contact time effect containing exponential type and consider moment of flexure contribute because The three-dimensional paralleling binding shear stress of son,The time effect containing exponential type that is contacted for i-th and consider the torque contribution factor Three-dimensional paralleling binding direct stress, f^sIndicate that rock mass carefully sees particle three-dimensional paralleling binding shear fracture criterion, f^sIt is indicated more than or equal to 0 Three-dimensional paralleling binding shear fracture indicates that shear fracture does not occur for three-dimensional paralleling binding less than 0；fⁿIt is indicated more than or equal to 0 three-dimensional Paralleling binding tensile fracture indicates that tensile fracture does not occur for three-dimensional paralleling binding less than 0；

Step 9：If the f in the formula (27) of step 8^sOr fⁿMore than or equal to 0, show that three-dimensional bonding is ruptured, this Rock mass carefully sees the spatial movement pattern of particle using the linear contact model for considering damping effect to express afterwards；If step F in 8 formula (27)^sAnd fⁿBoth less than 0, show that three-dimensional bonding does not rupture, continues cycling through step 2 to 8, calculate, update, sentence Disconnected rock mass carefully sees the three-dimensional bond state of particle contact, until rock mass does not generate new three-dimensional bonding rupture or three-dimensional bond is broken It splits accelerated development and forms macroscopic failure (by monitoring rock mass macroscopic deformation or strain, observing whether the value accelerates to judge), Loop termination.

In the step 2 of above-mentioned technical proposal, the rock mass carefully sees the parallel grain of particle three-dimensional and bonds the first of timeliness decaying deterioration The determination of beginning time step increment Delta t is the exponential type using the three-dimensional bonding timeliness deterioration decaying for considering bending contribution effect Pattern bonds the time be lost of decaying rupture for the first time to determine by the three-dimensional in each time step, namely passes through first three It ties up to bond and carries out the time divided by until first three-dimensional bonding rupture is required that decaying rupture is lasted by exponential type pattern Cycle-index is calculated to estimate initial time step-length, sees formula

Wherein, n_cRequired cycle calculations number is ruptured for first three-dimensional bond, For The three-dimensional of i-th of contact bonds diameter multiplier,To judge that three-dimensional rock mass carefully sees stress when particle starts timeliness deterioration decaying Threshold values,Particles parallel, which is carefully seen, for three-dimensional rock mass bonds tensile strength,Three-dimensional rock mass to consider the torque contribution factor is thin Particles parallel bond stress ratio is seen,Particle three-dimensional bond stress, β are carefully seen for rock mass₁In order to control in the rock mass of index overall variation Carefully see particle three-dimensional paralleling binding timeliness deterioration factor, β in portion₂It is thin inside the rock mass of index subscript part variation in order to control to see particle Three-dimensional paralleling binding timeliness deterioration factor,Particle three-dimensional paralleling binding, which is carefully seen, for three-dimensional rock mass deteriorates the straight of decaying at any time Diameter,Diameter when particle three-dimensional paralleling binding is not decayed, β are carefully seen for three-dimensional rock mass_σFor three under corresponding tensile strength state Dimension bonds timeliness and deteriorates the factor, β_τTimeliness, which is bonded, for the three-dimensional under corresponding shear strength state deteriorates the factor.

In above-mentioned technical proposal, the β_σTimeliness, which is bonded, for the three-dimensional under corresponding tensile strength state deteriorates the factor, β_τIt is right The determination that the three-dimensional under shear strength state bonds the timeliness deterioration factor is answered to include the following steps, wherein to include in these steps Formula subscript 1 represent first by exponential type pattern carry out timeliness decaying deterioration three-dimensional bond rupture label；

Step 1000：Speed, angular velocity difference and given cycle meter that particle three-dimensional bonds both ends particle are carefully seen by rock mass Calculate step Δ t_c, pass through formulaDetermine the normal direction relative rotation of three-dimensional bonded contactPass through FormulaDetermine the three-dimensional relative rotation for bonding the tangential directions ssPass through formulaDetermine the three-dimensional relative rotation for bonding the tangential directions stPass through formulaDetermine three-dimensional bonding normal direction incremental displacementPass through formulaDetermine the three-dimensional incremental displacement for bonding the tangential directions ssPass through formulaDetermine the three-dimensional incremental displacement for bonding the tangential directions stPass through formulaThe moment of flexure increment for determining three-dimensional bonded contact, passes through formulaIt determines Three-dimensional bonds the torque increase in the tangential directions st, passes through formulaDetermine the three-dimensional tangential side ss of bonding To torque increase.

Step 1001：According to the formula in step 1000Pass through formulaDetermine three-dimensional bonding normal force；According to the formula in step 1000And formulaPass through formulaWithDetermine the tangential st direction force of three-dimensional bonding, the tangential directions ss Power, and pass throughDetermine three-dimensional bond tangentially with joint efforts；According to the formula in step 1000And formulaPass through formulaIt determines Three-dimensional bonds normal direction moment of flexure；According to the formula in step 1000And formulaAndAnd formulaIt is logical Cross formulaAnd formulaThe determining three-dimensional bonding tangential directions st torque, The tangential directions ss torque, and pass throughDetermine that three-dimensional bond tangentially closes torque.In formula ,+ =it is the reflexive operator of addition, -=is the reflexive operator of subtraction.

Step 1002：Pass through formulaIt determines three-dimensional bonding mormal stress, passes through FormulaDetermine it is three-dimensional bond shear stress, by A, I, J in the two formula andWith A', I', J' andIt replaces, then substitutes into the formula (6) in the formula (7) in step 4~formula (9) and step 3, can get Including the three-dimensional of exponential type time effect and bending contribution effect bonds mormal stress calculation formulaTangential shearing stress calculation formula is bonded with three-dimensional

Step 1003：It willSubstitute into formulaAnd enable β=β_σ； It willSubstitute into formulaAnd enable β=β_τ, accordingly, can be respectively by formula According to Newton iteration Method or Stefansson Accelerated iteration method or second-class method solve the two equations, can respectively obtain under corresponding tensile strength state Three-dimensional bonds timeliness and deteriorates factor-beta_σ, and the three-dimensional bonding timeliness deterioration factor-beta under corresponding shear strength state_τ。

In above-mentioned technical proposal, the rock mass carefully see particle three-dimensional bonding rupture after, rock mass carefully sees the sky of particle Between motor pattern using considering that the linear contact model of damping effect expresses, for carefully being seen after describing rock mass season cracking The triaxiality and 3 D deformation and spatial movement rule of particle.Consider the structure packet of the linear contact model of damping effect Include following steps.

Step 2000：By Monte Carlo searching algorithms, traversal find rock mass carefully see each linear contact end a of particle, The centre coordinate of two-dimensional linear contact jaw b (particle and particle, particle and wall) is calculated under three-dimensional situation by formula (28) The two centre distance：

Wherein：D is the centre distance between linear contact both ends particle and particle or particle and wall,For the coordinate of linear contact jaw a,For the coordinate of linear contact jaw b；

Step 2001：Season cracking model is seen constructed three-dimensional is thin, in rock mass between particle each contact point list Bit vector is calculated by formula (29), if it is the contact between particle and particle, then utilizes the three-dimensional obtained in step 2000 Center point coordinate (the wherein coordinate of linear contact jaw a at linear contact both endsLinear contact jaw The coordinate of b) and centre distance d calculate the unit vector of each contact point between particle in rock mass；If it is particle It contacts with wall, is directly calculated using the normal vector equivalence replacement of wall, determine the unit vector of each contact point：

Wherein：n_iFor linear contact unit vector,For the direction vector of linear contact jaw b,It is three The direction vector of dimensional linear contact jaw a, n_wallTo constrain the direction vector of wall；

Step 2002：In the constructed thin sight season cracking model of three-dimensional, after rock masses fracturing, each contact point connects Lap U is touched, the center between both ends particle and particle or particle and wall is contacted by the linear that step 2000 calculates The distance d and particle radius R of linear contact both ends (ends a, the ends b)^a、R^b, formula (30) is recycled to determine；By setting Determine particle three-dimensional linear contact reference distance g_r, and formula (31) is combined, determine the distance g of particle three-dimensional linear contact_s：

g_s=| U |-g_r (31)

Step 2003：Season cracking model is seen constructed three-dimensional is thin, determines that carefully to see particle three-dimensional in rock mass linear Point contact method is to, tangential equivalent stiffness, using contact both ends particle entities or the rigidity k of wall^a, k^bIt is equivalent instead of connecing The normal stiffness and shear stiffness of contact are calculated by formula (32)：

Wherein：K_n、K_sFor equivalent normal stiffness and shear stiffness,For particle and particle or particle and wall Contact a ends normal stiffness and shear stiffness,The normal direction at the ends contact b for particle with particle or particle with wall Rigidity and shear stiffness；

Step 2004：In the constructed thin sight season cracking model of three-dimensional, determine that contact both ends are intergranular in rock mass Speed of related movement calculates, wherein e using formula (33), formula (34)_pqzFor Ricci index alternators, according to public affairs Formula (35) calculates：

Wherein：V_pWith V_qEquivalence, V_pWith V_qCarefully to see the intergranular relative motion in particle three-dimensional linear contact both ends in rock mass Speed, p, q are index symbol of equivalence, and p=1, q=1 indicate that particle is contacted with particle, and expression particle connects with wall when p=2, q=2 It touches,It is the speed of contact b end unit of the particle with particle or particle with wall,For particle The speed of contact a end units with particle or particle with wall,It is contact of the particle with particle or particle with wall The angular speed of a end units,It is the angular speed of contact b end unit of the particle with particle or particle with wall,For The displacement at contact a end of the particle with particle or particle with wall,It is contact b end of the particle with particle or particle with wall Displacement,For drift index transformation middle transition symbol,Indicate pellet-pellet or particle-wall when index symbol is p Contact a ends speed,Indicate the speed at the ends contact a of pellet-pellet or particle-wall when index symbol is q,Table Show the speed at the ends contact b of pellet-pellet or particle-wall when index symbol is p,Indicate particle-when index symbol is q The speed (the only ends a and two, the ends b contact jaw) at the ends contact b of particle or particle-wall；

Step 2005：Season cracking model is seen constructed three-dimensional is thin, it, can be with for the value of time step Δ t Minimum time step Δ t is obtained by formula (38), it is ensured that the calculating time step of constructed model is less than the value, you can protect Card system integral calculating tends towards stability, and is each linearly connect by formula (39), formula (40), formula (42), formula (43) determination Tactile total displacement increment, Normal Displacement increment and tangential displacement increment：

R=min (R_a,R_b) (36)

ΔU_p1=V_p1Δt (39)

Δδ_ss=Δ δ_sn_ss (42)

Δδ_st=Δ δ_sn_st (43)

Wherein：M is that rock mass carefully sees granular mass, and J1 is the rotary inertia that rock mass carefully sees particle；k^{It is flat}Particle is carefully seen for rock mass System translational stiffness, k^TurnParticle system rotational stiffness is carefully seen for rock mass；ΔU_p1The total of particle three-dimensional linear contact is carefully seen for rock mass Displacement increment, Δ δ_n、The Normal Displacement increment of particle three-dimensional linear contact, Δ δ are carefully seen for rock mass_s、It is thin for rock mass See the tangential displacement increment of particle three-dimensional linear contact, V_p1With V_q1The speed of related movement at particle contact both ends is carefully seen for rock mass, N is unit normal vector, Δ δ_ss、Δδ_stFor tangential displacement Δ δ_sComponent in the directions ss, the directions st, the relationship between three are：n_ss、n_stThe tangential directions ss, the st in particle three-dimensional linear contact face are carefully seen for rock mass The unit vector in direction, p1, q1 are tensor index figure shift.

Step 2006：In the constructed thin sight season cracking model of three-dimensional, can particle in rock mass be judged by formula (31) Surface contact allows existing maximum distance, normal direction and tangential displacement updating factor is calculated by formula (44), in addition, rock mass is thin The update for seeing particle three-dimensional linear contact Normal Displacement increment is to use the Normal Displacement increment of back and multiplying for updating factor α Product obtains, and the update that rock mass carefully sees particle three-dimensional linear contact tangential displacement increment ss durection components is using the tangential of back Displacement increment ss durection components and the product of updating factor α obtain, and rock mass carefully sees particle three-dimensional linear contact tangential displacement increment The update of st durection components is obtained using the tangential displacement increment st durection components of back and the product of updating factor α：

Wherein：(g_s)₀The surface that initial time is calculated for model contacts distance, g_sThe distance of particle contact is carefully seen for rock mass, α is displacement updating factor；

Step 2007：In the constructed thin sight season cracking model of three-dimensional, the update of three-dimensional normal direction linear force takes Relative vector adds up (M_l=1) and absolute vectors add up (M_l=0) pattern is calculated by formula (45), and tangential linear force is more It is new to use Three-Dimensional contact sliding to indicate, it is calculated by formula (48), formula (49)；

Wherein：k_n、k_sNormal direction linear rigidity, tangential linear rigidity, g are contacted for linear_sIt is model particle in certain lotus Surface under carrying contacts distance, Δ δ_nWith Δ δ_sRespectively linear contact normal direction displacement increment and tangential displacement increment, For linear contact normal direction contact force,For initial normal force increment size and tangential force increment size,It is three The tangential contact force of dimensional linear contact,For linear contact tangential linear force the directions st, the directions ss component, Relationship between three is: Stiction when particle does not slide is carefully seen for rock mass,For particle force of sliding friction, by friction coefficient μ withProduct obtains, Δ δ_st、Δδ_ssRespectively linear contact is cut To increment Delta δ_sIn the directions st displacement increment and the directions ss displacement increment, Δ δ_s、Δδ_st、Δδ_ssRelationship between three is：

Step 2008：In the constructed thin sight season cracking model of three-dimensional, normal direction damping force uses full normal mode M_d ={ 0,2 } and tensionless winkler foundation pattern M_dTwo kinds of={ 1,3 } is calculated by formula (50), formula (51)；Tangential damping force uses cuts entirely Cut pattern M_d={ 0,1 } and sliding cut-off-die formula M_d={ 2,3 } are calculated according to formula (52), formula (53)；

Wherein：The respectively normal direction and tangential damping force of linear contact, β_nFor linear contact Normal direction damped coefficient, β_sFor the tangential damped coefficient of linear contact, k_nNormal direction linear rigidity, k for linear contact_s For linear contact tangential linear rigidity,Respectively the normal direction rate of linear contact and linear connect Tactile tangential velocity, m_cFor equivalent particle quality, m⁽¹⁾The granular mass of the first contact jaw between particle and particle, m⁽²⁾For The granular mass of the second contact jaw between particle and particle, F^dFor linear contact total damping power,Respectively The tangential component damped in the directions ss, the directions st is contacted for linear, the relationship between three is: For linear contact normal direction contact force, It indicates Linear contacts the rate in the tangential directions ss,Indicate that linear contacts the rate in the tangential directions st,Relationship between three is：

Below using deep rock mass as example, the detailed process of the Numerical Implementation of model of the present invention is described in detail in conjunction with attached drawing, please be join The attached drawing during example figure illustrates is read, to understand the Numerical Implementation step and effect of model of the present invention：

Step 1, using C++ programming languages, and combine fish language, model structure according to the present invention builds flow chart (Figure 13) realizes Three-dimensional Rock on numerical value platform and carefully sees season cracking model；

Step 2, the rill evolution for primarily determining rock mass season cracking model

Grain size ratio Rratio, linear contact normal stiffness kn (Fig. 6), linear contact shear stiffness ks (Fig. 6), grain density Ba_rho, particle contact modulus b_Ec, paralleling binding normal stiffness pb_kn (Fig. 6), paralleling binding shear stiffness pb_ks (figures 6), paralleling binding model pb_Ec, the friction coefficient ba_fric of particle, the average value pb_sn_mean, viscous that bonds tensile strength Tie the standard deviation pb_sn_sdev of tensile strength, cohesive strength average value pb_coh_mean, cohesive strength standard deviation pb_coh_sdev, Paralleling binding radius multiplier gamma (Fig. 7), paralleling binding moment of flexure contribution factor beta_sigma, paralleling binding torque contribution because Sub- beta_shear, normal direction damped coefficient Apfan (Fig. 6), tangential damped coefficient Apfas (Fig. 6) and internal friction angle pb_phi 19 parameters such as (Fig. 8), parameter occurrence are shown in Table one；

Step 3 generates strata model

Normal direction adhesion strength and the distribution of tangential cohesive strength that model is determined according to Gaussian Profile or weibull distributions, pass through Uniformly random function distribution determines the particle diameter distribution of particle；Pass through isotropic stress adjusting method and adaptive dynamic swelling Method adjusts the position of particle, reduces particle lap；It by suspended particulate elimination method, deletes and isolates particle, improve model sample Globality, reduce the generation of defect model.Cast material adhesion strength parameter is finally assigned, generating has true rock mass structure Rock mass structure graph model.A diameter of 50mm of strata model, highly it is 100mm (Figure 14)；

The meso-damage evolution parameter of model in step 4, the Accurate Calibration present invention

The load-deformation curve obtained by indoor uniaxial and triaxial compression test, determines the macroscopic elastic modulus of rockPeak strength σ_pAnd Poisson's ratioBy optimization method, make the stress-of rock mass list, triaxial compressions model The stress-strain and macroscopic deformation Parameters and intensive parameter of strain curve and laboratory test coincide, and obtain constructed by the present invention The meso-damage evolution parameter of model；

Step 5, the calibration of rock mass timeliness mechanics parameter

The calibration of rock mass timeliness mechanics parameter carries out rock mass a series of timeliness mechanics examination under the conditions of different stress-strength ratios It tests, obtains the curve of rock mass deformation Temporal Evolution under the conditions of different stress-strength ratios.By parameter fitting method, practical rock is matched The secular distortion process of body determines that thin particle three-dimensional paralleling binding timeliness of seeing deteriorates system inside the rock mass of control characteristic overall variation Number β₁And thin sight particle three-dimensional paralleling binding timeliness deterioration factor β inside the rock mass of control characteristic subscript part variation₂；

Step 6, rock mass timeliness mechanics numerical experimentation

Under conditions of load is certain, different moment of flexure contribution factors and the torque contribution factor is set separately, carries out rock mass Three-dimensional thin sight timeliness mechanics numerical experiments (Figure 15), obtain shadow of the bending contribution factor to rock mass secular distortion and destruction Ring rule (Figure 16).

Table one：The parameter name and value of model of the present invention

The content that this specification is not described in detail belongs to the prior art well known to professional and technical personnel in the field.

Claims

1. a kind of three-dimensional season cracking model considering bending contribution effect, it is characterised in that：The three-dimensional season cracking model The rock mass for contributing the rock mass of effect carefully to see particle three-dimensional paralleling binding stress mode, consider Torsion Coupling effect including considering bending It is thin to see particle three-dimensional paralleling binding timeliness deterioration damped expoential pattern formula, consider Torsion Coupling effect and rubbing with stretching cut-off limit Your coulomb carefully sees particles parallel and bonds season cracking criterion and consider the thin sight particle three-dimensional linear contact model of damping effect；

Consider that torque carefully sees rock mass the percentage contribution of particle three-dimensional paralleling binding direct stress, effect is contributed in the consideration bending Rock mass carefully see particle three-dimensional paralleling binding stress mode be rock mass carefully see particle three-dimensional paralleling binding direct stress calculation formulaIn be provided with the torque contribution factor

Consider that moment of flexure carefully sees rock mass the percentage contribution of particle three-dimensional paralleling binding shear stress, in the rock for considering that effect is contributed in bending Body carefully sees the rock mass in particle three-dimensional paralleling binding stress mode and carefully sees particle three-dimensional paralleling binding Calculation Shear formulaIn be provided with moment of flexure contribution factor

Above-mentionedWithCalculation formula in,Particle three-dimensional paralleling binding radius is carefully seen for rock mass,To be used to determine torsion The torque contribution factor of percentage contribution of the square in stress, For for determining contribution journey of the moment of flexure in stress The moment of flexure contribution factor of degree,I is the moment of inertia that rock mass carefully sees particle three-dimensional paralleling binding, and J is that rock mass carefully sees particle The polar moment of inertia of three-dimensional paralleling binding, A are that rock mass carefully sees particle three-dimensional paralleling binding area；

The direct stress of particle three-dimensional paralleling binding is carefully seen for i-th of rock mass,It is parallel viscous that particle three-dimensional is carefully seen for i-th of rock mass The shear stress of knot,The rock mass of respectively i-th contact carefully sees particle three-dimensional paralleling binding normal direction Power, tangential resultant force, tangential conjunction torque and normal direction moment of flexure, wherein+=symbol is the reflexive operator of addition, In, in formula,The displacement increment of particle three-dimensional paralleling binding normal direction is carefully seen for rock mass,It is flat that particle three-dimensional is carefully seen for rock mass Row bonds normal stiffness, and A is that rock mass carefully sees particle three-dimensional paralleling binding area,In formula,Respectively rock mass carefully sees the tangential ss direction force of particle three-dimensional paralleling binding, tangential st direction force, wherein ss and st For the code name of orthogonal both direction on same plane；In formula,Respectively The tangential directions the ss torque of particle three-dimensional paralleling binding, the tangential directions st torque are carefully seen for rock mass；=symbol For the reflexive operator of subtraction, in formula,The relative rotation increment of particle three-dimensional paralleling binding normal direction is carefully seen for rock mass,For Rock mass carefully sees particle three-dimensional paralleling binding shear stiffness.

2. the three-dimensional season cracking model according to claim 1 for considering bending contribution effect, it is characterised in that：It is described to examine The three-dimensional season cracking model for considering bending contribution effect is suitable for three dimensional particles DEM analysis method, three dimensional particles discontinuously become Conformal analysis method and three dimensional particles manifold element method.

3. the three-dimensional season cracking model according to claim 1 for considering bending contribution effect, it is characterised in that：It is described to examine The rock mass for considering Torsion Coupling effect carefully sees particle three-dimensional paralleling binding timeliness deterioration damped expoential pattern formula, is included in rock mass and carefully sees When particles parallel bonds timeliness deterioration decaying, it is provided with exponential type and considers that the paralleling binding stress of bending contribution factor is relevant Rock mass carefully sees particle three-dimensional paralleling binding deterioration evanescent mode, sees exponential type turnover rateIn formula,To judge carefully to see particle three-dimensional paralleling binding by rock mass, to start timeliness bad Change stress threshold values when decaying,Particle three-dimensional paralleling binding tensile strength is carefully seen for rock mass,For consider bending contribution because The three-dimensional paralleling binding stress ratio of son, β₁It is thin inside the rock mass of index overall variation in order to control to see particle three-dimensional paralleling binding timeliness Deterioration factor, β₂It is thin inside the rock mass of index subscript part variation in order to control to see particle three-dimensional paralleling binding timeliness deterioration factor, e For the truth of a matter of natural logrithm；

It is arranged in considering that the rock mass of Torsion Coupling effect carefully sees particle three-dimensional paralleling binding timeliness deterioration damped expoential pattern formula The gradually deterioration decaying and related to the paralleling binding stress of bending contribution factor is considered at any time of three-dimensional paralleling binding diameter Exponential type pattern, see three-dimensional paralleling binding diameter formulaFormula In,The diameter that particle three-dimensional paralleling binding deteriorates decaying at any time is carefully seen for rock mass,It is parallel that particle three-dimensional is carefully seen for rock mass Diameter when not decaying is bonded, Δ t is the incremental time that rock mass carefully sees the decaying deterioration of particle three-dimensional paralleling binding timeliness；

Consider that the rock mass of Torsion Coupling effect is carefully seen in particle three-dimensional paralleling binding timeliness deterioration damped expoential pattern formula to be provided with Rock mass carefully sees the timeliness deterioration evanescent mode of particle three-dimensional paralleling binding area, the moment of inertia and polar moment of inertia, sees that consideration is viscous respectively Tie three-dimensional paralleling binding areal calculation formula when unit thickness is 1Bond three-dimensional when unit thickness is 1 Paralleling binding the moment of inertia calculation formulaBond three-dimensional paralleling binding polar moment of inertia meter when unit thickness is 1 Calculate formulaWherein, β is the timeliness decay factor that rock mass carefully sees particle three-dimensional paralleling binding diameter, meter Formula is calculated to seeWherein,A'、I'、J′、Be expressed as rock mass carefully see particle three-dimensional paralleling binding deteriorate at any time decaying bonding diameter, Radius, bond area are bonded, the moment of inertia is bonded, bond polar moment of inertia and bonds diameter multiplier,A、I、J、Carefully seen for rock mass bonding diameter when particle three-dimensional paralleling binding is not decayed, bond radius, bond area, bond the moment of inertia, It bonds polar moment of inertia and bonds diameter multiplier, while obtaining rock mass according to this three-dimensional exponential type timeliness deterioration evanescent mode and carefully seeing Particles parallel bonds the initial time step-length of rupture, sees formulaWherein, It is connect for i-th Tactile rock mass carefully sees particle three-dimensional paralleling binding diameter multiplier, n_cParticle three-dimensional paralleling binding, which is carefully seen, for first rock mass ruptures institute The number of the cycle calculations needed, β_σFor the rock mass under corresponding tensile strength state carefully see the deterioration of particle three-dimensional paralleling binding timeliness because Son, β_τParticle three-dimensional paralleling binding timeliness is carefully seen for the rock mass under corresponding shear strength state and deteriorates the factor, and e is natural logrithm The truth of a matter, ∞ are infinity, and rock mass carefully sees the deterioration factor-beta of the timeliness under particle three-dimensional paralleling binding tensile strength state_σAnd rock mass The thin timeliness seen under particle three-dimensional paralleling binding shear strength state deteriorates factor-beta_τIt can be respectively by formula：WithRoot The two equations are solved according to iterative method or second-class method to obtain, whereinParticle three-dimensional paralleling binding knot is carefully seen for rock mass to stretch by force Degree,The cohesive strength of particle three-dimensional paralleling binding is carefully seen for rock mass,The interior friction of particle three-dimensional paralleling binding is carefully seen for rock mass Angle, F_σFor β_σFunction, F_τFor β_τFunction, π is pi；

The rock mass of respectively i-th contact carefully sees particle three-dimensional paralleling binding normal force, tangential conjunction Power, tangential conjunction torque and normal direction moment of flexure.

4. the three-dimensional season cracking model according to claim 1 for considering bending contribution effect, it is characterised in that：Described Consider Torsion Coupling effect and carefully see particles parallel to bond season cracking criterion with mole coulomb for stretching cut-off limit to refer to sentencing When disconnected rock mass carefully sees particle three-dimensional paralleling binding season cracking, end using embedded consideration bending contribution effect and with stretching Mole coulomb season cracking criterion of limit judges, sees formula

Wherein,Respectively rock mass carefully sees particle three-dimensional paralleling binding tensile strength, shearing strength,It is connect for i-th The rock mass of tactile time effect containing exponential type and consideration moment of flexure contribution factor carefully sees particle three-dimensional paralleling binding direct stress, calculates public Formula is The time effect containing exponential type contacted for i-th and consideration torque tribute The rock mass for offering the factor carefully sees particle three-dimensional paralleling binding shear stress, and calculation formula is Exponential type time effect is contained in the three-dimensional paralleling binding stress of the criterion, sees that rock mass carefully sees particle three-dimensional paralleling binding diameter Timeliness decay factor calculation formulaf^sIt is carefully seen more than or equal to 0 expression rock mass Particle three-dimensional paralleling binding shear fracture, f^sParticle three-dimensional paralleling binding is carefully seen less than 0 expression rock mass, and shear fracture does not occur；fⁿ Particle three-dimensional paralleling binding tensile fracture, f are carefully seen more than or equal to 0 expression rock massⁿIt is parallel that particle three-dimensional is carefully seen less than 0 expression rock mass Tensile fracture does not occur for bonding；

The internal friction angle of particle three-dimensional paralleling binding is carefully seen for rock mass,The adhesive aggregation of particle three-dimensional paralleling binding is carefully seen for rock mass Power,Bonding radius when particle three-dimensional paralleling binding is not decayed is carefully seen for rock mass,Respectively i-th The rock mass of a contact carefully sees particle three-dimensional paralleling binding normal force, tangential resultant force, tangential conjunction torque and normal direction moment of flexure,Indicate rock Body carefully sees the bonding diameter that particle three-dimensional paralleling binding deteriorates decaying at any time,Rock mass carefully sees particle three-dimensional paralleling binding and does not decline Bonding diameter when subtracting,To judge that rock mass carefully sees stress threshold values when particle three-dimensional paralleling binding starts timeliness deterioration decaying,Particle three-dimensional paralleling binding tensile strength is carefully seen for rock mass,To consider that the three-dimensional paralleling binding of bending contribution factor is answered Power ratio,Particle three-dimensional paralleling binding stress is carefully seen for rock mass.

5. the three-dimensional season cracking model according to claim 1 for considering bending contribution effect, it is characterised in that：It is described to examine Considering the rock mass of damping effect, carefully to see particle three-dimensional linear contact model refer to rock mass after season cracking, is referred to by Three-Dimensional contact Distance g_rIt sets thin particle space of seeing inside rock mass and contacts distance, consider that the rock mass of damping effect is carefully seen particle three-dimensional and linearly connect Touch type is that thin particle space of seeing is contacted away from calculation formula inside rock massWherein, For the coordinate of contact jaw a,For the coordinate of contact jaw b, R^a、R^bThin for seeing contact jaw a respectively inside rock mass The particle radius of grain radius and contact jaw b；

Consider to be provided in the thin sight particle three-dimensional linear contact model of damping effect and considers that thin particle space of seeing becomes inside rock mass The linear contact mode of shape carefully sees the coupling work provided with consideration three-dimensional sliding friction surface power between particle inside rock mass With pattern, the thin linear Three-Dimensional contact normal direction linear force calculation formula for seeing particle space deformation in rock mass inside isTake M_l=1 is relative vector accumulation mode, takes M_l=0 is tired for absolute vectors Add pattern, the tangential linear force calculation formula of linear contact that particle space deformation is carefully seen inside rock mass isWithWherein,k_n、k_sThe linear contact of particle space deformation is carefully seen for rock mass inside Normal direction, tangential linear rigidity, Δ δ_nFor rock mass internal particle linear contact Normal Displacement increment,For rock The initial normal force increment size and tangential force increment size of internal portion particle three-dimensional linear contact,Exist for tangential linear force Thin see carefully sees the tangential side st of particle three-dimensional linear contact inside the tangential directions ss of particle three-dimensional linear contact and rock mass inside rock mass To component, ss and st are the code name of orthogonal both direction on same plane,For particle force of sliding friction, pass through Friction coefficient μ withProduct obtains,Stiction when not slided for particle, Δ δ_st、Δδ_ssIt is thin respectively inside rock mass to see It is thin inside the displacement increment and rock mass in the tangential directions ss of particle three-dimensional linear contact to see the tangential directions st of particle three-dimensional linear contact Displacement increment；

Consider that the thin of damping effect sees the space damping mode that Three-Dimensional contact is arranged in particle three-dimensional linear contact model simultaneously, Middle normal direction damping uses full normal mode M_d={ 0,2 } and tensionless winkler foundation pattern M_dTwo kinds of={ 1,3 }, passes through formulaIt calculates, wherein F^*For the contact of rock mass internal particle linear Full normal direction damping force, expression formula are The linear of particle space deformation is carefully seen for rock mass inside Contact normal direction linear force, m_cFor equivalent particle quality, by formulaIt calculates；

Tangential damping uses full shear mode M_d={ 0,1 } and sliding and shear mode M_d={ 2,3 }, according to formulaAnd formulaIt is calculated, In,The rate in the tangential directions ss is contacted for linear, ss is the directions ss in linear contact local coordinate system, Contact the rate in the tangential directions st for linear, st is that linear contacts directions st in local coordinate system, the directions st with The directions ss are mutually perpendicular to,For the normal direction damping force of rock mass internal particle linear contact, β_nIt is three-dimensional for rock mass internal particle Normal direction damped coefficient, the β of linear contact_sFor the tangential damped coefficient of rock mass internal particle linear contact, k_nFor rock mass inside Normal direction linear rigidity, the k of particle three-dimensional linear contact_sFor rock mass internal particle linear contact tangential linear rigidity, For rock mass internal particle linear contact normal direction rate,ForWithConjunction rate, referred to as linear contact Tangential velocity, the relationship between three is：m_cFor equivalent particle quality, m⁽¹⁾For rock mass inside The granular mass for the first contact jaw that grain is contacted with particle, m⁽²⁾The second contact jaw contacted with particle for rock mass internal particle Granular mass, F^dFor total damping power,For the tangential damping force of linear contact, F^dForResultant force, referred to as three Dimensional linear contacts total damping power, and triadic relation is： Tangentially to damp inside rock mass It is thin to see the thin component for seeing the tangential directions st of particle three-dimensional linear contact inside the tangential directions ss of particle three-dimensional linear contact and rock mass, g_rFor Three-Dimensional contact reference distance.