CN106844847B

CN106844847B - The thin construction method for seeing season cracking power function pattern type of rock mass two dimension

Info

Publication number: CN106844847B
Application number: CN201611161852.4A
Authority: CN
Inventors: 黄书岭; 丁秀丽; 李欢; 邬爱清; 徐平; 裴启涛; 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: 2018-01-23
Anticipated expiration: 2036-12-15
Also published as: CN106844847A

Abstract

The invention discloses the thin construction method for seeing season cracking power function pattern type of rock mass two dimension, the model includes considering that the rock mass of moment of flexure contribution factor carefully sees particle bond stress two-dimensional model, considers that the thin sight particle of moment of flexure contribution factor bonds the two-dimentional power function pattern formula of timeliness deterioration decay, considers moment of flexure contribution effect and mole coulomb with stretching cut-off limit carefully sees particle and bonds season cracking criterion, considers the thin sight particle linear contact two dimensional model of damping effect.The relation that the present invention is adapted between stress and crack propagation velocity meets this kind of rock mass of power function type, and technical support is provided for the prediction of country rock long-time stability, evaluation and the optimization design of this kind of deep rock mass engineering project under flat state.

Description

The thin construction method for seeing season cracking power function pattern type of rock mass two dimension

Technical field

Season cracking analysis technical field is carefully seen the present invention relates to engineering rock mass, is broken in particular to the thin timeliness of seeing of rock mass two dimension Split the construction method of power function pattern type.

Background technology

Unstability and destruction after deep rock mass engineering project excavation are frequently not to occur at once after excavation, are usually present Obvious deformation fracture is ageing and the hysteresis quality of catastrophe (rock burst, large deformation etc.), seriously endangers the construction safety and length of engineering Phase runs.At present, 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 text two-dimentional creep meso mechanical model of application is short-term to silk screen griotte and long-term strength feature is carried out Numerically modeling (rock-soil mechanics, 2013, Vol.34 No.12：3601-3608).This class model is to build driving stress with exponential type Relation between crack propagation velocity, for describing season cracking of the rock carefully in sight aspect, suitable for stress and Crack Extension This kind of rock mass of index of coincidence expression way between speed.In addition, also there is following weak point in this class model：(1) between particle Shear fracture criterion be a horizontal linear parallel with paralleling binding direct stress, namely this shear fracture criterion with it is parallel It is unrelated to bond direct stress state, as long as paralleling binding shear stress is more than or equal to fixed paralleling binding shear fracture intensity, Shear fracture can occur for intergranular, and can not embody different paralleling binding direct stress in rock mass has different paralleling binding shear fractures The objective fact of intensity；(2) do not account for bonding influence of the difference effect of torque to contact failure, the contribution of torque will be bonded The influence to different lithology is spent to be accordingly to be regarded as unanimously；(3) for not conforming to symbol index expression way between stress and crack propagation velocity Rock mass, this class model lack adaptability.

The content of the invention

It is an object of the invention to for drawbacks described above, it is proposed that a kind of rock mass two dimension is thin to see season cracking power function pattern The construction method of type, the model structure include considering that the rock mass of moment of flexure contribution factor is carefully seen particle bond stress two-dimensional model, examined Consider moment of flexure contribution factor thin sight particle bond timeliness deterioration decay two-dimentional power function pattern formula, consider moment of flexure contribution effect and Mole-coulomb with stretching cut-off limit carefully sees particle and bonds season cracking criterion and consider that the thin sight particle of damping effect linearly connects Touch two dimensional model.The relation that the present invention is adapted between stress and crack propagation velocity meets this kind of rock mass of power function type, right The prediction of country rock long-time stability, evaluation and the optimization design of this kind of deep rock mass engineering project provide technology branch under flat state Hold.

The purpose of the present invention is reached by following measure：The thin sight season cracking power function pattern type of rock mass two dimension Construction method, it is characterized in that, comprises the following steps：

Step 1：Set the thin geometric parameters quantity for seeing particle bonded contact inside rock mass, including particle bond area and particle Bond the moment of inertia, R^a、R^bParticle radius, the particle radius at b ends at respectively two-dimentional bonded contact a ends,Particle is carefully seen for rock mass Diameter multiplier or radius multiplier are bonded, under two-dimensional case, particle bond area A when unit thickness is 1 is bonded and bonds used Property square I is determined by formula (2), formula (3) respectively：

Wherein：Particle two dimension is carefully seen for rock mass and bonds radius,Particle two dimension is carefully seen for rock mass and bonds diameter multiplier or half Footpath multiplier, A are that rock mass carefully sees particle two dimension bond area, and I is that rock mass carefully sees particle two dimension bonding the moment of inertia；

Step 201：The initial time step size increments Δ t that particle two dimension bonds timeliness decay deterioration is carefully seen using rock mass, is led to Cross power function form calculus rock mass and carefully see the diameter that particle two dimension bonds timeliness decay deteriorationDetermined by formula (4)；

Wherein：To consider that the two dimension of moment of flexure contribution factor bonds normal stress,To judge that rock mass carefully sees particle two dimension Stress threshold values when starting timeliness deterioration decay is bonded,The tensile strength that particle two dimension bonds carefully is seen for rock mass,To examine Consider the two-dimentional bond stress ratio of moment of flexure contribution factor, β₁、β₂Respectively rock mass carefully sees the first control ginseng that particle bonds timeliness deterioration Number, the second control parameter,Particle two dimension is carefully seen for rock mass and bonds the diameter that decay is deteriorated with the time,Particle is carefully seen for rock mass Two dimension bonds diameter when not decaying, and Δ t is that rock mass carefully sees the incremental time that particle two dimension bonds timeliness decay deterioration；

Step 202：According to the formula (4) in step 201, the thin timeliness decay factor seen particle two dimension and bond diameter is set β, see formula (5)：

Wherein：A′、I′、It is expressed as rock mass and carefully sees the bonding that particle two dimension bonding deteriorates decay with the time Diameters, radius, bond area are bonded, the moment of inertia is bonded, bonds diameter multiplier,A、I、Carefully seen for rock mass Particle two dimension bonds bonding diameter, bonding radius, bond area, bonding the moment of inertia, the bonding diameter multiplier when not decaying；

Step 203：According to the formula (5) in the formula (1) in step 1~formula (3) and step 202, rock mass is set Thin particle two dimension of seeing bonds geometric parameter timeliness deterioration evanescent mode, and in the case of planar, it is viscous that rock mass carefully sees particle two dimension Knot diameter increases and constantly deteriorates decay over time, bonds area and the moment of inertia that particle when unit thickness is 1 bonds Increase over time and constantly deteriorate decay, see formula (6), formula (7) respectively；

Wherein：A ', I ' be expressed as rock mass carefully see particle two dimension bond with the time deteriorate decay bonding radius, Bond area, the moment of inertia is bonded, A, I are that rock mass carefully sees the two-dimentional bond area bonded when not decaying of particle, bonds the moment of inertia；

Step 204：The rock mass for calculating j-th to k-th successively carefully sees the two dimension bonding normal direction that particle includes time effect Moment of flexure increment, under two-dimensional case, by the speed, angular speed and the given cycle calculations time step increment that bond both ends particle Δ t, determine that i-th of rock mass carefully sees particle two dimension and bond relative rotation by formula (8), formula (9), formula (10)Rock Body carefully sees particle two dimension and bonds normal direction incremental displacementAnd rock mass carefully sees particle two dimension and bonds tangential incremental displacement In conjunction with the formula (5) in the formula (7) and step 202 in step 203, determine that i-th of rock mass is carefully seen particle and imitated comprising the time The two dimension answered bonds moment of flexure increment, is specifically shown in formula (11)；

Wherein：Ff, j, k, i are natural numbers, and 2≤j≤ff≤k, j are in each cycle calculations, include time effect Rock mass carefully sees particle two dimension and bonds uncracked initial index value after decay, and ff is middle index value, and k is each cycle calculations In, the rock mass comprising time effect carefully sees particle two dimension and bonds uncracked most end index value after decay, and i is first to last One two-dimentional bonded particulate index value,Respectively i-th of rock mass carefully sees particle two dimension bonded contact A ends and b ends absolute movement speed and angular speed, n_n、n_sRespectively rock mass carefully sees the normal direction list in particle two dimension bonded contact face Bit vector and tangential unit vector, Respectively rock mass carefully sees particle two dimension and bonds normal direction displacement increment and tangential position Move increment,Particle two dimension is carefully seen for rock mass and bonds normal stiffness,Particle two dimension is carefully seen for rock mass and bonds moment of flexure increment.

Step 205：Formula (8), formula (9) in the formula (6) and formula (7), step 204 in step 203 and Formula (5) in formula (11) and step 202, successively renewal calculate j-th to k-th rock mass and carefully see particle and bond and do not rupture Bonded contact and two dimension comprising time effect bond normal force, tangential force and tangential moment of flexure, pass through formula (12), formula (13), formula (14) calculates the bonding normal force, tangential force and tangential moment of flexure that i-th of rock mass carefully sees particle two dimension bonded contact, Under two-dimensional case, normal direction moment of flexure is bonded to determine that rock mass carefully sees particle by formula (15),

Normal force：

Tangential force：

Tangential moment of flexure：

Normal direction moment of flexure：

Wherein：Respectively i-th of rock mass carefully sees particle and includes time effect The bonding normal force answered, tangential force, the bonding normal direction moment of flexure comprising time effect are bonded, tangential moment of flexure is bonded, bonds normal direction position Move increment and bond tangential displacement increment,Particle two dimension is carefully seen for rock mass and bonds shear stiffness, +=is addition from inverse operation Symbol, -=is the reflexive operator of subtraction.

Step 206：Moment of flexure contribution factor is setConsider that moment of flexure particle bonding normal direction of seeing thin to rock mass is answered The percentage contribution of power, particle is carefully seen according to rock mass and bonds two-dimentional direct stress calculation formulaBonded with two dimension Calculation Shear formulaSimultaneously by A, I in the two formula andWith A ', I ' andReplace, then by step Formula (5) in formula (6) and formula (7) and step 202 in 203 substitutes into, obtain comprising power function type time effect and Thin particle bonding of seeing considers that the two dimension of moment of flexure contribution factor bonds direct stressCalculation formula and two dimension bond shear stressMeter Formula is calculated, sees formula (16) and formula (17) respectively,

Step 207：Time effect will be included in step 206Formula (18) is substituted into, it is determined that considering moment of flexure tribute Offer the factor and mole-coulomb with stretching cut-off limit carefully sees particle and bond season cracking criterion, and calculate successively j-th to the Whether k rock mass carefully sees particle two dimension bond stress, ruptured and fracture mode for judging that rock mass is carefully seen particle and bonded, The rock mass of the criterion, which is carefully seen, contains power function type time effect and consideration moment of flexure contribution factor in particle bond stress,

Wherein：f^s、fⁿRespectively rock mass carefully sees timeliness shear fracture criterion, the timeliness tensile fracture standard that particle two dimension bonds Then,Two dimension for the time effect of type containing power function of i-th of contact bonds shear stress,For containing for i-th of contact Power function type time effect and the two dimension bonding direct stress for considering moment of flexure contribution factor,Respectively rock mass carefully sees particle Tensile strength, the shearing strength of two dimension bonding,The cohesive strength that particle two dimension bonds carefully is seen for rock mass,Particle two is carefully seen for rock mass Tie up the internal friction angle of bonding；f^sParticle is carefully seen more than or equal to 0 expression rock mass and bonds shear fracture, and rock mass carefully sight is represented less than 0 Shear fracture does not occur for grain bonding；fⁿParticle is carefully seen more than or equal to 0 expression rock mass and bonds tensile fracture, represents that rock mass is thin less than 0 See particle and bond and tensile fracture does not occur；

Step 208：F in the formula (18) in step 207^sOr fⁿDuring more than or equal to 0, show that rock mass is carefully seen particle and glued Bind up one's hair raw rupture, now rock mass carefully sees the motor pattern of particle using the two-dimensional linear contact model of consideration damping effect come table Reach；F in the formula (18) in step 207^sAnd fⁿWhen both less than 0, show that rock mass is carefully seen particle and bonded and do not rupture, continue to follow Ring step 201 calculated, renewal, judges that rock mass carefully sees the bond state of particle contact to 207, up to rock mass do not produce it is new thin See the rupture of particle bonding or rock mass carefully sees particle and bonds rupture accelerated development and form macroscopic failure, loop termination.

Preferably, the rock mass carefully sees particle two dimension and bonds the initial time step size increments Δ t of timeliness decay deterioration really It is fixed, it is the two-dimentional power function pattern formula that timeliness deterioration decay is bonded using the thin sight particle for considering moment of flexure contribution factor, by each Thin sight particle two dimension in time step bonds decay first and ruptures the time be lost to determine, i.e., sees particle by first thin Bond and decay time for being lasted of rupture divided by until first thin see needed for particle bonds rupture as power function pattern formula The calculating cycle-index wanted estimates initial time step size increments Δ t, sees formulaWherein,For i-th of contact Rock mass carefully see particle two dimension and bond diameter multiplier, n_cParticle two dimension, which is carefully seen, for first rock mass bonds the required circulation meter of rupture The number of calculation, β_σ、β_τRespectively rock mass is carefully seen the timeliness deterioration factor, two dimension bonding corresponding to particle two dimension bonding tensile strength and cut Timeliness corresponding to shearing stress deteriorates the factor, and i is followed successively by first and carefully sees particle bonding number to last rock mass, and ∞ is infinite Greatly.

Preferably, the rock mass carefully sees particle two dimension and bonds timeliness deterioration factor-beta corresponding to tensile strength_σCarefully seen with rock mass Timeliness corresponding to particle two dimension bond shear strength deteriorates factor-beta_τDetermination comprise the following steps, wherein included in these steps Formula subscript 1 represent first by power function pattern formula carry out timeliness decay deterioration thin sight particle two dimension bond rupture mark Number：

Step 211：Under two-dimensional case, particle is carefully seen by rock mass and bonds the speed of both ends particle, angular speed and given Cycle calculations time step increment Delta t_c, pass through formulaIt is determined that carefully see the phase of particle bonded contact To cornerPass through formulaIt is determined that carefully seeing particle bonds normal direction incremental displacement Pass through formulaDetermine that particle bonds tangential incremental displacementPass through formulaDetermine the moment of flexure increment of particle bonded contact；

Step 212：According to the formula in step 211Pass through formulaIt is determined that carefully see the bonding normal force of particle contact；According to the formula in step 211Pass through formulaIt is determined that the bonding for carefully seeing particle contact is tangential Power；According to the formula in step 211And formulaPass through formulaIt is determined that carefully see the tangential moment of flexure of bonding of particle contact；Pass through formulaIt is determined that carefully see particle The bonding normal direction moment of flexure of contact, wherein, +=is the reflexive operator of addition, and -=is the reflexive operator of subtraction；

Step 213：Under two-dimensional case, pass through formulaIt is determined that carefully see particle contact Direct stress is bonded, passes through formulaIt is determined that carefully see particle contact bonding shear stress, by A, I in the two formula with AndWith A ', I ' andReplace, then by formula (5) generation in the formula (6) and formula (7) and step 202 in step 203 Enter, obtain thin particle of seeing and bond comprising power function type time effect and consider that the two dimension of moment of flexure contribution factor bonds direct stress and calculated FormulaCalculation Shear formula is bonded with the two dimension comprising power function type time effect

Step 214：WillSubstitute into formulaAnd make β=β_σ；WillSubstitute into formulaAnd make β=β_τ, accordingly, respectively obtain the rock mass and carefully see particle two dimension bonding drawing Stretch timeliness corresponding to intensity and deteriorate the factorAnd rock mass carefully sees particle Timeliness corresponding to two-dimentional bond shear strength deteriorates the factor

Preferably, the rock mass is carefully seen after particle bonds and rupture, and rock mass carefully sees the motor pattern of particle using considering The two-dimensional linear contact model of damping effect is expressed, and carefully seeing particle for describing rock mass bonds thin particle of seeing after season cracking Stress, deformation and moving law, consider that the structure of the two-dimensional linear contact model of damping effect comprises the following steps：

Step 301：By Monte Carlo searching algorithms, traversal finds rock mass and carefully sees each two-dimensional linear contact of particle A, two-dimensional linear contact jaw b (particle and particle, particle and wall) centre coordinate are held, under two-dimensional case, is passed through formula (19) Calculate contact point a ends, the centre distance at contact point b ends：

Wherein：D is the centre distance between two-dimensional linear contact both ends particle and particle or particle and wall,For Two-dimensional linear contact jaw a coordinate,For two-dimensional linear contact jaw b coordinate.

Step 302：Rock mass carefully sees the unit vector of each contact point between particle and passes through formula (20) under two-dimensional plane state Calculate, if the contact between particle and particle, utilize the center point coordinate that two-dimensional linear contact both ends are obtained in step 301 And apart from calculating；If particle contacts with wall, directly calculated using the normal vector equivalence replacement of wall；It is determined that each contact The unit vector at end：

Wherein：n_iFor the unit vector of contact,For contact jaw b direction vector,For contact jaw a direction vector, n_wallTo constrain the direction vector of wall；

Step 303：After rock mass carefully sees particle bonding rupture, the contact lap U of each two-dimensional linear contact point, pass through Step 301 calculates the grain spacing d and particle radius R at two-dimensional linear contact both ends^a、R^b, recycle formula (21) to determine； Reference distance g is contacted by setting particle two-dimensional linear_r, and formula (22) is combined, determine the distance of particle two-dimensional linear contact g_s：

g_s=| U |-g_r (22)

Step 304：Determine that rock mass carefully sees grain contact point normal direction, tangential equivalent stiffness, using contacting both ends particle entities Or the rigidity k of wall^a, k^bThe equivalent rigidity instead of contact point, calculated by formula (23)：

Wherein：K_n、K_sGrain contact point equivalent normal stiffness and shear stiffness are carefully seen for rock mass, For particle with The normal stiffness and shear stiffness at the contact a ends of particle or particle with wall,For particle and particle or particle and wall Contact b ends normal stiffness and shear stiffness.

Step 305：Determine to contact the intergranular speed of related movement in both ends in rock mass, utilize formula (24), formula (25) To calculate.Wherein e_pqzFor Ricci index alternators, calculated according to formula (26)：

Wherein：V_pWith V_qEquivalence, V_pWith V_qTo contact the intergranular speed of related movement in both ends in rock mass, p, q are index etc. Valency symbol, p=1, q=1 represent that particle contacts with particle, and expression particle contacts with wall when p=2, q=2,For The speed of particle and the contact b end units of particle or particle with wall,It is particle and particle or particle and wall Contact a end units speed,It is angular speed of the particle with the contact a end units of particle or particle with wall,It is angular speed of the particle with the contact b end units of particle or particle with wall,It is particle and particle or particle The displacement at the contact a ends with wall,It is displacement of the particle with the contact b ends of particle or particle with wall,Become for drift index The middle transition symbol changed,The speed at the contact a ends of pellet-pellet or particle-wall when index symbol is p is represented,Table Show the speed at the contact a ends of pellet-pellet or particle-wall when index symbol is q,Represent index symbol particle when being p- The speed at the contact b ends of particle or particle-wall,Represent the contact of pellet-pellet or particle-wall when index symbol is q The speed (only a ends and two, b ends contact jaw) at b ends.

Step 306：For the thin initial time step size increments Δ t for seeing particle linear contact model of rock mass value, pass through The minimum time step Δ t of formula (29) estimation, it is ensured that the calculating time step of constructed model is less than the value, you can ensures system System integral and calculating tends towards stability；The total displacement for determining each linear contact by formula (30), formula (31), formula (32) increases Amount, Normal Displacement increment and tangential displacement increment：

R=min (R_a, R_b) (27)

ΔU_p1=V_p1Δt (30)

Wherein：R is the equivalent redius that rock mass carefully sees particle, and m is that rock mass carefully sees granular mass, and J1 is that rock mass carefully sees particle Rotary inertia；k^{It is flat}Particle system translational stiffness, k are carefully seen for rock mass^TurnParticle system rotational stiffness is carefully seen for rock mass；ΔU_p1For rock mass The thin total displacement increment for seeing the contact of particle two-dimensional linear, Δ δ_n、Physical significance is identical, represents that rock mass carefully sees particle two dimension The Normal Displacement increment of linear contact, Δ δ_s、Physical significance is identical, represents that rock mass carefully sees the contact of particle two-dimensional linear Tangential displacement increment, V_p1With V_q1The speed of related movement at particle contact both ends is carefully seen for rock mass, n is unit normal vector, p1, q1 For tensor index figure shift.

Step 307：The ultimate range as existing for formula (22) judgement rock mass carefully sees particle surface contact permission, calculates normal direction With tangential displacement updating factor, in addition, the renewal that rock mass carefully sees particle two-dimensional linear contact normal direction displacement increment is using previous The Normal Displacement increment of step obtains with updating factor α product, and rock mass carefully sees particle two-dimensional linear contact tangential displacement increment Renewal is obtained using the tangential displacement increment of back and updating factor α product.

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 308：The normal direction linear force that rock mass carefully sees the contact of particle two-dimensional linear takes relative vector to add up (M_l=1) and Absolute vectors adds up (M_l=0) pattern, calculated and obtained by formula (33), (34)；Rock mass carefully sees the contact of particle two-dimensional linear Tangential linear force carefully sees particle contact slide using rock mass to represent, is calculated and obtained by formula (35)：

Wherein：Respectively rock mass carefully sees the two-dimensional linear contact normal direction linear force, tangential of stress deformation between particle Linear force, k_n、k_sRespectively rock mass carefully sees the two-dimensional linear contact normal direction of stress deformation between particle, tangential linear rigidity, Δ δ_n、 Δδ_sRespectively rock mass carefully sees the Normal Displacement increment of particle two-dimensional linear contact, tangential displacement increment,Respectively Initial normal force increment size, the tangential force increment size of particle two-dimensional linear contact are carefully seen for rock mass,Particle is carefully seen for rock mass not Stiction during slip,Particle force of sliding friction is carefully seen for rock mass, its value can by friction coefficient μ withProduct obtains.

Step 309：The normal direction damping that rock mass carefully sees particle linear contact uses full normal mode M_d={ 0,2 } and tensionless winkler foundation Pattern M_dTwo kinds of={ 1,3 }, calculated by formula (36), wherein m_cFor equivalent particle quality, calculated by formula (37), rock mass is thin The tangential damping for seeing particle linear contact uses full shear mode M_d={ 0,1 } and cunning-cut-off-die formula M_d={ 2,3 }, according to formula (38) calculate,

Wherein：Respectively rock mass carefully sees the linear damping force of normal direction, the tangential linear damping of particle linear contact Power, β_nThe normal direction damped coefficient of particle linear contact, β are carefully seen for rock mass_sThe tangential damping system of particle linear contact is carefully seen for rock mass Number, k_nThe normal direction linear rigidity of particle linear contact, k are carefully seen for rock mass_sThe tangential linear firm of particle linear contact is carefully seen for rock mass Degree,Respectively rock mass carefully sees the normal direction speed and tangential velocity of particle linear contact, F^*It is linear that particle is carefully seen for rock mass The full normal direction damping force of contact, expression formula arem_cEquivalent particle quality, m are carefully seen for rock mass⁽¹⁾For rock mass The thin thin sight granular mass for seeing particle contact jaw 1, m⁽²⁾The thin sight granular mass of particle contact jaw 2, F are carefully seen for rock mass^dFor rock mass The thin total damping power for seeing particle linear contact.

A kind of rock mass two dimension proposed by the invention is thin to see season cracking power function pattern type and construction method, and it is beneficial to effect Fruit and advantage are mainly reflected in：

(1) rock mass is carefully seen in particle bonding direct stress two dimension calculation formula and is provided with moment of flexure contribution factor in the present invention, no Only account for moment of flexure and the percentage contribution of direct stress is bonded to thin particle of seeing, and also contemplate shadow of the moment of flexure to rock mass long-term strength Ring, be adapted to the mesomechanics fracture behaviour of rock mass under description plane stress or plane strain condition.

(2) constructed in the present invention and consider that the thin sight particle of moment of flexure contribution factor bonds the two-dimentional power letter of timeliness deterioration decay Number pattern formula, when being included in rock mass and carefully seeing particle and bond timeliness deterioration decay, there is provided power function type with consider moment of flexure contribution because The thin sight particle of the bond stress correlation of son bonds two dimension deterioration evanescent mode, and there is provided thin sight particle bonding is progressively bad with the time Change the two-dimensional model of decay, there is provided the thin area and cross sectional moment of inertia timeliness deterioration decay two-dimensional model seen particle and bonded；Together When according to this timeliness deterioration evanescent mode estimation rock mass carefully see particle bond rupture initial time step-length.This power function type Forming types are adapted to the mesomechanics season cracking mechanism and response pattern for describing a kind of deep rock mass under flat state.

(3) it is embedded to consider moment of flexure contribution in the present invention in the constructed thin sight season cracking power function pattern type of two dimension Effect and mole-coulomb limited with stretching cut-off carefully see particle and bond season cracking criterion.When rock mass is carefully seen particle and bonded During effect rupture, effect is contributed using embedded consideration moment of flexure and ends mole-coulomb season cracking criterion of limit with stretching To judge；Power function type time effect is included in the criterion particle bond stress and adds moment of flexure contribution factor, not only may be used To describe the difference of timeliness shear fracture intensity related to particle bonding direct stress, it is reasonable that timeliness tensile fracture can also be carried out Expression, and consider moment of flexure to bond season cracking influence, meet a kind of rock mass under planar condition and carefully see season cracking mould Formula.

(4) it is embedded to consider damping effect in the present invention in the constructed thin sight season cracking power function pattern type of two dimension Thin sight particle linear contact two dimensional model structure, after rock mass season cracking, pass through specify two dimensional touch reference distance set Rock mass carefully sees interparticle contact distance, sets and considers that rock mass carefully sees between particle the two dimensional touch pattern of stress deformation and in rock mass The binding mode for considering two-dimentional sliding friction is set between thin sight particle, while the damping mode of two dimensional touch is set, can be reasonable Particle motion and stress characteristic of a kind of deep engineering rock mass after season cracking under planar condition are described.

Brief 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 that particle overlap condition schematic diagram is carefully seen in model of the present invention.

Fig. 4 is that particle Rigidity Calculation schematic diagram is carefully seen 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 that the linear adhesive structure schematic diagram of particle is carefully seen in model of the present invention.

Fig. 8 is that moment of flexure contribution effect is considered in model of the present invention and carefully sees particle with mole-coulomb that stretching cut-off limits Bond season cracking criterion schematic diagram.

Fig. 9 is carefully to see particle in model of the present invention to bond diameter (or radius) timeliness deterioration decay schematic diagram.

Figure 10 is that the normal direction in particle two dimensional touch face and tangential unit vector schematic diagram are carefully seen in model of the present invention.

Figure 11 is the schematic flow sheet of the construction method of model of the present invention.

Figure 12 is model basic model sample of the present invention

Figure 13 is model creeping displacement and time history of the present invention

In figure：1 represents the centre distance d of two particles, and 2, which represent rock mass, carefully sees intergranular half contact distance, and 3 represent rock mass Carefully see intergranular half reference distance g_r, 4 represent the coordinate that rock mass carefully sees particle a, and 5 represent the coordinate that rock mass carefully sees particle b, and 6 Rock mass carefully sees the centre coordinate of particle surface contact distance, and 7, which represent rock mass, carefully sees particle surface contact distance g_s, 8 represent rock mass Intergranular contact unit normal vector is carefully seen, 9 represent the radius R that rock mass carefully sees particle a^a, 10 represent half that rock mass carefully sees particle b Footpath R^b, 11 represent the contact lap U that rock mass carefully sees grain contact point, and 12 represent the firm of b (rock mass particle or border wall) Degree (normal direction, shear stiffness are referred to as) k^b, 13 represent rigidity (normal direction, the shear stiffness system of a (rock mass particle or border wall) Claim) k^a, 14 represent the equivalent stiffness that rock mass carefully sees grain contact point, and 15 represent total displacement increment Delta U_i, 16 represent initial normal forceIncrement size, 17 representatives initially contact force vectors and 18 represent initial tangential forceIncrement size, 19 represent constructed two Tie up season cracking model normal direction displacement increment Δ δ_nOr20, which represent constructed two-dimentional season cracking model tangential displacement, increases Measure Δ δ_sOr21 represent the tensile strength that rock mass carefully sees particle bonding22 represent rock mass carefully see particle bond normal direction it is firm Degree23 represent the normal stiffness K that rock mass carefully sees grain contact point_n, 24, which represent rock mass, carefully sees particle bonding shear stiffness25 Represent rock mass and carefully see particle bond shear strength, 25.1 representThe cohesive strength of particle bonding is carefully seen for rock mass, 25.2 represent rock mass Thin particle of seeing bonds internal friction angle26 represent the shear stiffness K that rock mass carefully sees grain contact point_s, 27, which represent rock mass, carefully sees particle The linear contact coefficient of sliding friction, 28, which represent rock mass, carefully sees particle linear contact normal direction damped coefficient β_n, 29, which represent rock mass, carefully sees The tangential damped coefficient β of particle linear contact_s, 30, which are represented as rock mass, carefully sees particle bonding radius multiplier31 represent rock mass carefully sight Grain bonds diameter32 represent consideration moment of flexure contribution effect and end mole-coulomb season cracking criterion of limit with stretching, and 33 Represent the bonding shear stress comprising time effect of i-th of contact34 represent including time effect and examining for i-th of contact Consider the bonding direct stress of moment of flexure contribution factor35, which represent rock mass, carefully sees the radius that particle bonds timeliness decay36 represent Rock mass carefully sees the diameter that particle bonds timeliness decay37, which represent rock mass, carefully sees particle and bonds diameter when not decaying38 generations Table rock mass carefully sees radius when particle bonding does not decay39 represent the normal vector n that rock mass carefully sees particle contact surface_n, 40 represent Rock mass carefully sees the tangential unit vector n of particle contact surface_s。

Embodiment

Below in conjunction with the accompanying drawings with specific construction step and embodiment, model of the present invention is explained in detail.Example Illustrate it is only understanding of the auxiliary for the present invention, the practical ranges without limiting the present invention.After the present invention has been read, Modification of the those skilled in the art to the various equivalent form of values of the present invention belongs to the apllied claim of the present invention and limited Fixed scope.

Note：Formula has been write exactly before all labels in specification, is formula label such as formula (1).

As shown in Fig. 1~Figure 10, rock mass two dimension of the present invention is thin to see season cracking power function pattern type, is adapted to two Tie up granular discrete-element, Particles in Two Dimensions discontinuous deformation analysis, Particles in Two Dimensions manifold member；It is curved that power function pattern type includes consideration When the rock mass of square contribution factor carefully sees particle bond stress two-dimensional model, the rock mass of consideration moment of flexure contribution factor carefully sees particle bonding The two-dimentional power function pattern formula of effect deterioration decay, consider that moment of flexure contributes effect and mole-coulomb carefully sight with stretching cut-off limit Grain bonds season cracking criterion and considers the thin sight particle linear contact two dimensional model of damping effect.

Consider that the rock mass of moment of flexure contribution factor carefully sees particle bond stress two-dimensional model and refers to that rock mass is carefully seen particle and bonded just Stress two dimension calculation formulaIn be provided with moment of flexure contribution factorConsider moment of flexure to the thin sight particle of rock mass Two dimension bonds the percentage contribution of direct stress；Above-mentionedIn formula,Particle two dimension, which is carefully seen, for i-th of rock mass bonds direct stress,The rock mass of respectively i-th contact carefully sees particle two dimension and bonds normal force, tangential moment of flexure,Particle is carefully seen for rock mass Two dimension bonds radius,For moment of flexure contribution factor,I is that rock mass carefully sees the moment of inertia that particle two dimension bonds, and A is rock mass Thin to see particle two dimension bond area, i, which is followed successively by first and carefully sees particle to last rock mass, bonds number.The rock of i-th of contact Body carefully sees particle two dimension and bonds normal forceBond tangential moment of flexureComputational methods be：Normal force In formula,Particle two dimension is carefully seen for rock mass and bonds normal direction displacement increment,Particle two dimension is carefully seen for rock mass and bonds normal stiffness, Tangential moment of flexureIn formula,Particle two dimension is carefully seen for rock mass and bonds circumferentially opposite rotating angle increment, +=is to add The reflexive operator of method, -=is the reflexive operator of subtraction, normal direction moment of flexure

Consider that the rock mass of moment of flexure contribution factor is carefully seen the two-dimentional power function pattern formula that particle bonding timeliness deterioration decays and included When rock mass carefully sees particle two dimension and bonds timeliness deterioration decay, there is provided related to considering the bond stress of moment of flexure contribution factor Power function pattern formula, the thin sight particle two dimension in this power function pattern formula bond diameter and decay are progressively deteriorated with the time, see viscous Diameter formula is tied,

In formula,Particle two dimension is carefully seen for rock mass and bonds the diameter that decay is deteriorated with the time,Particle two is carefully seen for rock mass Dimension bonds diameter when not decaying,To consider that the two dimension of moment of flexure contribution factor bonds normal stress,To judge that rock mass is carefully seen Particle two dimension bonds stress threshold values when starting timeliness deterioration decay,The tensile strength that particle two dimension bonds carefully is seen for rock mass,To consider the two-dimentional bond stress ratio of moment of flexure contribution factor, β₁、β₂It is bad that particle two dimension bonding timeliness is carefully seen for control rock mass Two designated indexs changed, Δ t are that rock mass carefully sees the incremental time that particle two dimension bonds timeliness decay deterioration；It is thin there is provided rock mass Particle bond area and face the moment of inertia timeliness deterioration decay two-dimensional model are seen, sees that rock mass when cohesive unit thickness is 1 is thin respectively See the bond area calculation formula that particle deteriorates decay with the timeBond the moment of inertia I ' when unit thickness is 1 Calculation formulaWherein, β is that rock mass carefully sees the timeliness decay factor that particle two dimension bonds diameter, and it is calculated Formula is shown in

Wherein,A′、I′、It is expressed as rock mass and carefully sees the bonding that particle two dimension bonding deteriorates decay with the time Diameters, radius, bond area are bonded, the moment of inertia is bonded, bonds diameter multiplier,A、I、Carefully seen for rock mass Particle bonds bonding diameter, bonding radius, bond area, bonding the moment of inertia, the bonding diameter multiplier when not decaying；While according to This power function type timeliness deterioration evanescent mode estimation rock mass carefully sees the initial time step delta t that particle bonds rupture, sees formula

Wherein,Particle two dimension bonding diameter multiplier is carefully seen for the rock mass of i-th of contact, n_cThe number of the cycle calculations needed for particle two dimension bonding rupture, β are carefully seen for first rock mass_σ、β_τRespectively rock mass carefully sees particle Two dimension bonds the timeliness deterioration factor corresponding to tensile strength, the timeliness deterioration factor corresponding to two-dimentional bond shear strength, and i is followed successively by Particle carefully being seen to last rock mass for first and bonding number, ∞ is infinity.

Rock mass carefully sees particle two dimension and bonds timeliness deterioration factor-beta corresponding to tensile strength_σWith two-dimentional bond shear strength pair The timeliness deterioration factor-beta answered_τCalculation formula be respectively

Wherein,Bonding normal force, tangential force and the bonding that respectively i-th of particle contacts are tangential curved Square,Particle two dimension is carefully seen for rock mass and bonds tensile strength,The cohesive strength that particle two dimension bonds carefully is seen for rock mass,For rock mass The thin internal friction angle seen particle two dimension and bonded.

Consideration moment of flexure contributes effect and the thin sight particle of mole-coulomb with stretching cut-off limit bonds season cracking criterion and referred to When rock mass carefully sees particle two dimension and bonds season cracking, effect is contributed using embedded consideration moment of flexure and ends limit with stretching Mole-coulomb season cracking criterion judges, sees formula

Its In, f^s、fⁿRespectively rock mass carefully sees timeliness shear fracture criterion, the timeliness tensile fracture criterion that particle two dimension bonds, Respectively rock mass carefully sees particle two dimension and bonds tensile strength, shearing strength,Respectively i-th contact contains power The rock mass of function type time effect and consideration moment of flexure contribution factor carefully sees particle two dimension and bonds direct stress, shear stress.

The time effect of type containing power function of i-th of contact and the rock mass of consideration moment of flexure contribution factor are carefully seen particle two dimension and bonded The calculation formula of direct stress is

I-th contact the time effect of type containing power function rock mass carefully see particle two dimension bond shear stress calculation formula be

Power function type time effect is contained in the two-dimentional bond stress of the criterion, sees that rock mass is carefully seen particle two dimension and bonded The timeliness decay factor β calculation formula of diameter

β₁、β₂Respectively control rock mass carefully sees particle and bonds timeliness deterioration The first control parameter, the second control parameter；f^sParticle two dimension is carefully seen more than or equal to 0 expression rock mass and bonds shear fracture, less than 0 Represent that rock mass carefully sees particle two dimension bonding and shear fracture does not occur；fⁿParticle two dimension, which is carefully seen, more than or equal to 0 expression rock mass bonds drawing Rupture is stretched, carefully seeing particle two dimension bonding less than 0 expression rock mass, tensile fracture does not occur.

Consider that the thin sight particle linear contact two dimensional model of damping effect refers to that carefully seeing particle in rock mass bonds season cracking Afterwards, reference distance g is contacted by given two-dimensional linear_rParticle two-dimensional linear contact distance g is seen there is provided thin_s, see that rock mass is carefully seen Particle two-dimensional linear is contacted away from calculation formula

Wherein,For rock mass internal particle and particle two-dimensional linear contact jaw a coordinate,For rock mass inside The coordinate of particle and particle two-dimensional linear contact jaw b, R^a、R^bRespectively rock mass carefully see two-dimensional linear contact jaw a particle radius and Two-dimensional linear contact jaw b particle radius；The two-dimensional linear contact mode deformed between particle is carefully seen there is provided consideration rock mass, in rock Body carefully sees the binding mode for being provided between particle and considering two-dimentional sliding friction line power, and rock mass carefully sees two of stress deformation between particle Dimensional linear contacts normal direction linear force calculation formulaTake M_l=1 adds up for relative vector Pattern, take M_l=0 is absolute vectors accumulation mode, and rock mass carefully sees the tangential linear force of two-dimensional linear contact of stress deformation between particle Calculation formula isWherein,Respectively rock mass carefully sees two of stress deformation between particle Dimensional linear contact normal direction linear force, tangential linear force, k_n、k_sRespectively rock mass is carefully seen the two-dimensional linear of stress deformation between particle and connect Touch normal direction, tangential linear rigidity, Δ δ_n、Δδ_sRespectively Normal Displacement increment, tangential displacement increment,Respectively Initial normal force increment size and tangential force increment size,Stiction when not slided for particle, Particle force of sliding friction is carefully seen for rock mass, by friction coefficient μ withProduct obtains；

The damping of the damping mode for setting two-dimensional linear to contact simultaneously, wherein normal direction uses full normal mode M_d={ 0,2 } and Tensionless winkler foundation pattern M_dTwo kinds of={ 1,3 }, passes through formulaCalculate, wherein m_cFor equivalent Grain quality, by formulaCalculate, tangential damping uses full shear mode M_d={ 0,1 } and sliding- Cut-off-die formula M_d={ 2,3 }, according to formulaTo calculate, wherein：Respectively method To damping force, tangential damping force, β_nFor normal direction damped coefficient, β_sFor tangential damped coefficient, k_nFor normal direction linear rigidity, k_sTo cut To linear rigidity,For normal direction speed, tangential velocity, m_cFor equivalent particle quality.F^*Particle is carefully seen for rock mass linearly to connect Tactile full normal direction damping force, expression formula arem⁽¹⁾For the granular mass of two-dimensional linear contact jaw 1, m⁽²⁾ For the granular mass of two-dimensional linear contact jaw 2.

As shown in figure 11, the thin construction method for seeing season cracking power function pattern type of rock mass two dimension of the present invention, bag Include following steps：

Wherein, rock mass carefully sees the determination that particle two dimension bonds the initial time step size increments Δ t of timeliness decay deterioration, is to adopt The two-dimentional power function pattern formula of timeliness deterioration decay is bonded with the thin sight particle for considering moment of flexure contribution factor, by each time step Thin sight particle two dimension bond decay first and rupture time be lost to determine, i.e., by it is first thin see particle and bond press power Function type pattern carries out time divided by until the first thin calculating seen required for particle bonding ruptures that decay rupture is lasted Cycle-index estimates initial time step size increments Δ t, sees formula

Wherein,For The rock mass of i contact carefully sees particle two dimension and bonds diameter multiplier, n_cParticle two dimension is carefully seen for first rock mass to bond needed for rupture Cycle calculations number, β_σ、β_τRespectively rock mass carefully sees particle two dimension and bonds the timeliness deterioration factor, two corresponding to tensile strength Tie up bond shear strength corresponding to timeliness deterioration the factor, i be followed successively by first to last rock mass carefully see particle bond number, ∞ For infinity.

Rock mass carefully sees particle two dimension and bonds timeliness deterioration factor-beta corresponding to tensile strength_σIt is viscous that particle two dimension is carefully seen with rock mass Tie timeliness deterioration factor-beta corresponding to shear strength_τDetermination comprise the following steps, the formula subscript wherein included in these steps 1, which represents first thin sight particle two dimension that timeliness decay deterioration is carried out by power function pattern formula, bonds rupture label：

Step 214：WillSubstitute into formulaAnd make β=β_σ；WillSubstitute into formulaAnd make β=β_σ, accordingly, respectively obtain the rock mass and carefully see particle two dimension bonding drawing Stretch timeliness corresponding to intensity and deteriorate the factorAnd rock mass carefully sees particle Timeliness corresponding to two-dimentional bond shear strength deteriorates the factor

Normal force：

Tangential force：

Tangential moment of flexure：

Normal direction moment of flexure：

The rock mass is carefully seen after particle bonds and rupture, and rock mass carefully sees the motor pattern of particle using considering damping effect Two-dimensional linear contact model express, carefully seeing particle for describing rock mass bonds the thin stress for seeing particle after season cracking, becomes Shape and moving law, consider that the structure of the two-dimensional linear contact model of damping effect comprises the following steps：

g_s=| U |-g_r (22)

R=min (R_a, R_b) (27)

ΔU_p1=V_p1Δt (30)

Below using deep rock mass as example, the detailed process of the Numerical Implementation of model of the present invention is described in detail with reference to accompanying drawing, please be join Figure 12 to Figure 13 during example figure illustrates and Fig. 1 to Figure 10 in model brief description of the drawings is read, to understand model of the present invention Numerical Implementation step and effect：

Step 1：Using C++ programming languages, and fish language is combined, flow chart is built according to the model structure of the present invention (Figure 11), the thin sight season cracking power function pattern type of rock mass two dimension is realized on numerical value platform.

Step 2：Primarily determine that the rill evolution of rock mass season cracking model

Particle diameter is than Rratio, linear contact normal stiffness kn (Fig. 6), linear contact shear stiffness ks (Fig. 6), grain density Ba_rho, particle contact modulus b_Ec, normal stiffness pb_kn (Fig. 6) is bonded, shear stiffness pb_ks (Fig. 6) is bonded, bonds mould Type pb_Ec, the coefficient of friction ba_fric of particle, the average value pb_sn_mean for bonding tensile strength, the mark of bonding tensile strength Accurate poor pb_sn_sdev, cohesive strength average value pb_coh_mean, cohesive strength standard deviation pb_coh_sdev, bonding radius multiplier Gamma (Fig. 7), bond moment of flexure devotion factor beta, normal direction damped coefficient Apfan (Fig. 6), tangential damped coefficient Apfas (Fig. 6) And 19 parameters such as internal friction angle pb_phi (Fig. 8), parameter occurrence are shown in Table one.

Step 3：Generate strata model

Bonding tensile strength and the cohesive strength distribution of model are determined according to Gaussian Profile or weibull distributions, by uniform Distribution of random function method determines the particle diameter distribution of particle；By isotropic stress adjusting method and adaptive dynamic swelling method, adjust The position of whole particle, reduce particle lap；By suspended particulate elimination method, isolated particle is deleted, improves the whole of model sample Body, reduce the generation of defect model.Finally assign cast material adhesion strength parameter, rock of the generation with true rock mass structure Body Model.A diameter of 50mm of strata model, highly it is 100mm (Figure 12).

Step 4：The meso-damage evolution parameter of model in the Accurate Calibration present invention

The load-deformation curve obtained by indoor single shaft and triaxial compression test, determine the macroscopic elastic modulus of rock massPeak strength σ_p, and Poisson's ratioBy optimization method, make rock mass list, triaxial compressions model stress- 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：Rock mass timeliness mechanics parameter is demarcated

A series of timeliness mechanical test under the conditions of different stress-strength ratios is carried out to rock mass, obtains different stress-strength ratios Under the conditions of rock mass deformation Temporal Evolution curve.By parameter fitting method, the secular distortion process of actual rock mass is matched, it is determined that Rock mass carefully sees the first control parameter β that particle bonds timeliness deterioration₁, the second control parameter β₂。

Step 6：Rock mass timeliness mechanics numerical experimentation

Under conditions of load is certain, different moment of flexure contribution factors is set respectively, obtains rock mass secular distortion destruction Evolution (Figure 13).

The parameter name and value of model of the present invention are as shown in Table 1.

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

In above-described embodiment, the symbol and the symbol in Fig. 1~Figure 10 and brief description of the drawings of formula are mutually corresponding.

Other unspecified parts are prior art, and all of above parameter can be by consulting handbook or calculating Arrive.The present invention is not strictly limited to above-described embodiment.The particular embodiment of the present invention is the foregoing is only, is not used to limit The system present invention.Any modification, equivalent substitution and improvement for being made within the spirit and principles of the invention etc., all in the present invention Protection domain within.

Claims

1. the thin construction method for seeing season cracking power function pattern type of rock mass two dimension, it is characterised in that comprise the following steps：

Step 1：The thin geometric parameters quantity for seeing particle bonded contact inside rock mass is set, including particle bond area and particle bond The moment of inertia, R^a、R^bParticle radius, the particle radius at b ends at respectively two-dimentional bonded contact a ends,Particle bonding is carefully seen for rock mass Diameter multiplier or radius multiplier, under two-dimensional case, bond particle bond area A when unit thickness is 1 and bond the moment of inertia I Determined respectively by formula (2), formula (3)：

<mrow> <mover> <mi>R</mi> <mo>&OverBar;</mo> </mover> <mo>=</mo> <mover> <mi>&lambda;</mi> <mo>&OverBar;</mo> </mover> <mi>min</mi> <mrow> <mo>(</mo> <msup> <mi>R</mi> <mi>a</mi> </msup> <mo>,</mo> <msup> <mi>R</mi> <mi>b</mi> </msup> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow>

<mrow> <mi>A</mi> <mo>=</mo> <mn>2</mn> <mover> <mi>R</mi> <mo>&OverBar;</mo> </mover> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> </mrow>

<mrow> <mi>I</mi> <mo>=</mo> <mfrac> <mn>2</mn> <mn>3</mn> </mfrac> <msup> <mover> <mi>R</mi> <mo>&OverBar;</mo> </mover> <mn>3</mn> </msup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> </mrow>

Wherein：Particle two dimension is carefully seen for rock mass and bonds radius,Particle two dimension bonding diameter multiplier is carefully seen for rock mass or radius multiplies Number, A are that rock mass carefully sees particle two dimension bond area, and I is that rock mass carefully sees particle two dimension bonding the moment of inertia；

Step 201：The initial time step size increments Δ t that particle two dimension bonds timeliness decay deterioration is carefully seen using rock mass, passes through power Functional form calculates rock mass and carefully sees the diameter that particle two dimension bonds timeliness decay deteriorationDetermined by formula (4)；

<mrow> <msup> <mover> <mi>D</mi> <mo>&OverBar;</mo> </mover> <mo>&prime;</mo> </msup> <mo>=</mo> <mover> <mi>D</mi> <mo>&OverBar;</mo> </mover> <mo>-</mo> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <mn>0</mn> <mo>,</mo> <mover> <mi>&sigma;</mi> <mo>&OverBar;</mo> </mover> <mo><</mo> <msub> <mover> <mi>&sigma;</mi> <mo>&OverBar;</mo> </mover> <mrow> <mi>a</mi> <mi>a</mi> </mrow> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>&beta;</mi> <mn>1</mn> </msub> <msup> <mrow> <mo>(</mo> <mfrac> <mover> <mi>&sigma;</mi> <mo>&OverBar;</mo> </mover> <msub> <mover> <mi>&sigma;</mi> <mo>&OverBar;</mo> </mover> <mi>c</mi> </msub> </mfrac> <mo>)</mo> </mrow> <msub> <mi>&beta;</mi> <mn>2</mn> </msub> </msup> <mi>&Delta;</mi> <mi>t</mi> <mo>,</mo> <msub> <mover> <mi>&sigma;</mi> <mo>&OverBar;</mo> </mover> <mrow> <mi>a</mi> <mi>a</mi> </mrow> </msub> <mo>&le;</mo> <mover> <mi>&sigma;</mi> <mo>&OverBar;</mo> </mover> <mo><</mo> <msub> <mover> <mi>&sigma;</mi> <mo>&OverBar;</mo> </mover> <mi>c</mi> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>4</mn> <mo>)</mo> </mrow> </mrow>

Wherein：To consider that the two dimension of moment of flexure contribution factor bonds normal stress,Bonded to judge that rock mass carefully sees particle two dimension Start stress threshold during timeliness deterioration decay,The tensile strength that particle two dimension bonds carefully is seen for rock mass,It is curved to consider The two-dimentional bond stress ratio of square contribution factor, β₁、β₂Respectively rock mass carefully see particle bond timeliness deterioration the first control parameter, Second control parameter,Particle two dimension is carefully seen for rock mass and bonds the diameter that decay is deteriorated with the time,Particle two is carefully seen for rock mass Dimension bonds diameter when not decaying, and Δ t is that rock mass carefully sees the initial time step size increments that particle two dimension bonds timeliness decay deterioration；

Step 202：According to the formula (4) in step 201, the thin timeliness decay factor β for seeing particle two dimension and bonding diameter is set, is seen Formula (5)：

<mrow> <mi>&beta;</mi> <mo>=</mo> <msup> <mover> <mi>D</mi> <mo>&OverBar;</mo> </mover> <mo>&prime;</mo> </msup> <mo>/</mo> <mover> <mi>D</mi> <mo>&OverBar;</mo> </mover> <mo>=</mo> <msup> <mover> <mi>R</mi> <mo>&OverBar;</mo> </mover> <mo>&prime;</mo> </msup> <mo>/</mo> <mover> <mi>R</mi> <mo>&OverBar;</mo> </mover> <mo>=</mo> <msup> <mover> <mi>&lambda;</mi> <mo>&OverBar;</mo> </mover> <mo>&prime;</mo> </msup> <mo>/</mo> <mover> <mi>&lambda;</mi> <mo>&OverBar;</mo> </mover> <mo>=</mo> <mn>1</mn> <mo>-</mo> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <mn>0</mn> <mo>,</mo> <mover> <mi>&sigma;</mi> <mo>&OverBar;</mo> </mover> <mo><</mo> <msub> <mover> <mi>&sigma;</mi> <mo>&OverBar;</mo> </mover> <mrow> <mi>a</mi> <mi>a</mi> </mrow> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>&beta;</mi> <mn>1</mn> </msub> <msup> <mrow> <mo>(</mo> <mfrac> <mover> <mi>&sigma;</mi> <mo>&OverBar;</mo> </mover> <msub> <mover> <mi>&sigma;</mi> <mo>&OverBar;</mo> </mover> <mi>c</mi> </msub> </mfrac> <mo>)</mo> </mrow> <msub> <mi>&beta;</mi> <mn>2</mn> </msub> </msup> <mfrac> <mrow> <mi>&Delta;</mi> <mi>t</mi> </mrow> <mover> <mi>D</mi> <mo>&OverBar;</mo> </mover> </mfrac> <mo>,</mo> <msub> <mover> <mi>&sigma;</mi> <mo>&OverBar;</mo> </mover> <mrow> <mi>a</mi> <mi>a</mi> </mrow> </msub> <mo>&le;</mo> <mover> <mi>&sigma;</mi> <mo>&OverBar;</mo> </mover> <mo><</mo> <msub> <mover> <mi>&sigma;</mi> <mo>&OverBar;</mo> </mover> <mi>c</mi> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>5</mn> <mo>)</mo> </mrow> </mrow>

Wherein：A'、I'、Be expressed as rock mass carefully see particle two dimension bond with the time deteriorate decay bonding it is straight Footpaths, radius, bond area are bonded, the moment of inertia is bonded, bonds diameter multiplier,A、I、Carefully seen for rock mass The two-dimentional bonding diameter bonded when not decaying of grain, radius, bond area are bonded, the moment of inertia is bonded, bonds diameter multiplier；

Step 203：According to the formula (5) in the formula (1) in step 1~formula (3) and step 202, setting rock mass is carefully seen Particle two dimension bonds geometric parameter timeliness deterioration evanescent mode, and in the case of planar, it is straight that rock mass carefully sees particle two dimension bonding Footpath increases and constantly deteriorates decay over time, bond unit thickness be 1 when particle bond area and the moment of inertia also with Time increases and constantly deteriorates decay, sees formula (6), formula (7) respectively；

<mrow> <msup> <mi>A</mi> <mo>&prime;</mo> </msup> <mo>=</mo> <mn>2</mn> <msup> <mover> <mi>R</mi> <mo>&OverBar;</mo> </mover> <mo>&prime;</mo> </msup> <mo>=</mo> <mi>&beta;</mi> <mi>A</mi> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>6</mn> <mo>)</mo> </mrow> </mrow>

<mrow> <msup> <mi>I</mi> <mo>&prime;</mo> </msup> <mo>=</mo> <mfrac> <mn>2</mn> <mn>3</mn> </mfrac> <msup> <mover> <mi>R</mi> <mo>&OverBar;</mo> </mover> <mrow> <mo>&prime;</mo> <mn>3</mn> </mrow> </msup> <mo>=</mo> <msup> <mi>&beta;</mi> <mn>3</mn> </msup> <mi>I</mi> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>7</mn> <mo>)</mo> </mrow> </mrow>

Wherein：A', I' are expressed as rock mass and carefully see bonding radius, adhesive surface that particle two dimension bonding deteriorates decay with the time Product, the moment of inertia is bonded, A, I are that rock mass carefully sees the two-dimentional bond area bonded when not decaying of particle, bonds the moment of inertia；

Step 204：The rock mass for calculating j-th to k-th successively carefully sees the two dimension bonding normal direction moment of flexure that particle includes time effect Increment, under two-dimensional case, by bonding speed, angular speed and the given cycle calculations time step increment Delta t of both ends particle, Determine that i-th of rock mass carefully sees particle two dimension and bond relative rotation by formula (8), formula (9), formula (10)Rock mass is thin See particle two dimension and bond normal direction incremental displacementAnd rock mass carefully sees particle two dimension and bonds tangential incremental displacementTie again The formula (5) in the formula (7) and step 202 in step 203 is closed, determines that i-th of rock mass carefully sees particle and include time effect Two dimension bonds moment of flexure increment, is specifically shown in formula (11)；

<mrow> <msub> <mrow> <mo>(</mo> <msubsup> <mi>&Delta;U</mi> <mi>i</mi> <mi>n</mi> </msubsup> <mo>)</mo> </mrow> <mrow> <mi>f</mi> <mi>f</mi> </mrow> </msub> <mo>=</mo> <mrow> <mo>(</mo> <msubsup> <mover> <mi>X</mi> <mo>&CenterDot;</mo> </mover> <mi>i</mi> <mi>b</mi> </msubsup> <mo>-</mo> <msubsup> <mover> <mi>X</mi> <mo>&CenterDot;</mo> </mover> <mi>i</mi> <mi>a</mi> </msubsup> <mo>)</mo> </mrow> <msub> <mi>n</mi> <mi>n</mi> </msub> <msub> <mi>&Delta;t</mi> <mi>c</mi> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>8</mn> <mo>)</mo> </mrow> </mrow>

<mrow> <msub> <mrow> <mo>(</mo> <msubsup> <mi>&Delta;U</mi> <mi>i</mi> <mi>s</mi> </msubsup> <mo>)</mo> </mrow> <mrow> <mi>f</mi> <mi>f</mi> </mrow> </msub> <mo>=</mo> <mrow> <mo>(</mo> <msubsup> <mover> <mi>X</mi> <mo>&CenterDot;</mo> </mover> <mi>i</mi> <mi>b</mi> </msubsup> <mo>-</mo> <msubsup> <mover> <mi>X</mi> <mo>&CenterDot;</mo> </mover> <mi>i</mi> <mi>a</mi> </msubsup> <mo>)</mo> </mrow> <msub> <mi>n</mi> <mi>s</mi> </msub> <msub> <mi>&Delta;t</mi> <mi>c</mi> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>9</mn> <mo>)</mo> </mrow> </mrow>

<mrow> <msub> <mrow> <mo>(</mo> <msubsup> <mi>&Delta;&theta;</mi> <mi>i</mi> <mi>n</mi> </msubsup> <mo>)</mo> </mrow> <mrow> <mi>f</mi> <mi>f</mi> </mrow> </msub> <mo>=</mo> <mrow> <mo>(</mo> <msubsup> <mi>&omega;</mi> <mi>i</mi> <mi>b</mi> </msubsup> <mo>-</mo> <msubsup> <mi>&omega;</mi> <mi>i</mi> <mi>a</mi> </msubsup> <mo>)</mo> </mrow> <msub> <mi>&Delta;t</mi> <mi>c</mi> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>10</mn> <mo>)</mo> </mrow> </mrow>

<mrow> <msub> <mrow> <mo>(</mo> <mi>&Delta;</mi> <msup> <msub> <mover> <mi>M</mi> <mo>&OverBar;</mo> </mover> <mi>i</mi> </msub> <mi>s</mi> </msup> <mo>)</mo> </mrow> <mrow> <mi>f</mi> <mi>f</mi> </mrow> </msub> <mo>=</mo> <msub> <mover> <mi>k</mi> <mo>&OverBar;</mo> </mover> <mi>n</mi> </msub> <msup> <mi>&beta;</mi> <mn>3</mn> </msup> <mi>I</mi> <msub> <mrow> <mo>(</mo> <msubsup> <mi>&Delta;&theta;</mi> <mi>i</mi> <mi>n</mi> </msubsup> <mo>)</mo> </mrow> <mrow> <mi>f</mi> <mi>f</mi> </mrow> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>11</mn> <mo>)</mo> </mrow> </mrow>

Wherein：Ff, j, k, i are natural numbers, and 2≤j≤ff≤k, j are the rock mass comprising time effect in each cycle calculations Thin particle two dimension of seeing bonds uncracked initial index value after decay, and ff is middle index value, and k is bag in each cycle calculations Rock mass containing time effect carefully sees particle two dimension and bonds uncracked most end index value after decay, and i is first to last Two-dimentional bonded particulate index value,Respectively i-th of rock mass carefully sees a ends of particle two dimension bonded contact With the absolute movement speed and angular speed at b ends, n_n、n_sRespectively rock mass carefully see the normal direction unit in particle two dimension bonded contact face to Amount and tangential unit vector, Respectively rock mass carefully sees particle two dimension and bonds normal direction displacement increment and tangential displacement Increment,Particle two dimension is carefully seen for rock mass and bonds normal stiffness,Particle two dimension is carefully seen for rock mass and bonds moment of flexure increment；

Step 205：Formula (8), formula (9) and formula in the formula (6) and formula (7), step 204 in step 203 (11) formula (5) and in step 202, successively renewal calculate j-th to k-th rock mass carefully see particle bond it is uncracked viscous Knot contact and two dimension comprising time effect bonds normal force, tangential force and tangential moment of flexure, by formula (12), formula (13), Formula (14) calculates the bonding normal force, tangential force and tangential moment of flexure that i-th of rock mass carefully sees particle two dimension bonded contact, in two dimension In the case of, normal direction moment of flexure is bonded to determine that rock mass carefully sees particle by formula (15),

Normal force：

Tangential force：

Tangential moment of flexure：

Normal direction moment of flexure：

Wherein：Respectively i-th of rock mass carefully sees particle and includes time effect Normal force is bonded, tangential force, the bonding normal direction moment of flexure comprising time effect is bonded, bonds tangential moment of flexure, bonds Normal Displacement increasing Amount and bonding tangential displacement increment,Particle two dimension is carefully seen for rock mass and bonds shear stiffness, +=is the reflexive operator of addition, -= For the reflexive operator of subtraction；

Step 206：Moment of flexure contribution factor is setConsider that moment of flexure particle of seeing thin to rock mass bonds normal stress Percentage contribution, particle is carefully seen according to rock mass and bonds two-dimentional direct stress calculation formulaBond to cut with two dimension and answer Power calculation formulaSimultaneously by A, I in the two formula andWith A', I' andReplace, then by step 203 Formula (6) and formula (7) and step 202 in formula (5) substitute into, obtain comprising power function type time effect and thin see Grain, which bonds, considers that the two dimension of moment of flexure contribution factor bonds direct stressCalculation formula and two dimension bond shear stressCalculate public Formula, formula (16) and formula (17) are seen respectively,

<mrow> <msub> <msup> <mrow> <mo>(</mo> <mover> <msub> <mi>&sigma;</mi> <mi>i</mi> </msub> <mo>&OverBar;</mo> </mover> <mo>)</mo> </mrow> <mo>&prime;</mo> </msup> <mrow> <mi>f</mi> <mi>f</mi> </mrow> </msub> <mo>=</mo> <mfrac> <mn>1</mn> <mrow> <mn>2</mn> <mi>&beta;</mi> <mover> <mi>R</mi> <mo>&OverBar;</mo> </mover> </mrow> </mfrac> <mrow> <mo>(</mo> <mo>-</mo> <msub> <mrow> <mo>(</mo> <msup> <mover> <msub> <mi>F</mi> <mi>i</mi> </msub> <mo>&OverBar;</mo> </mover> <mi>n</mi> </msup> <mo>)</mo> </mrow> <mrow> <mi>f</mi> <mi>f</mi> </mrow> </msub> <mo>+</mo> <mfrac> <mrow> <mn>3</mn> <mover> <mi>&beta;</mi> <mo>&OverBar;</mo> </mover> <mo>|</mo> <msub> <mrow> <mo>(</mo> <msup> <mover> <msub> <mi>M</mi> <mi>i</mi> </msub> <mo>&OverBar;</mo> </mover> <mi>s</mi> </msup> <mo>)</mo> </mrow> <mrow> <mi>f</mi> <mi>f</mi> </mrow> </msub> <mo>|</mo> </mrow> <mrow> <mi>&beta;</mi> <mover> <mi>R</mi> <mo>&OverBar;</mo> </mover> </mrow> </mfrac> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>16</mn> <mo>)</mo> </mrow> </mrow>

<mrow> <msub> <msup> <mrow> <mo>(</mo> <mover> <msub> <mi>&tau;</mi> <mi>i</mi> </msub> <mo>&OverBar;</mo> </mover> <mo>)</mo> </mrow> <mo>&prime;</mo> </msup> <mrow> <mi>f</mi> <mi>f</mi> </mrow> </msub> <mo>=</mo> <mfrac> <mrow> <mo>|</mo> <msub> <mrow> <mo>(</mo> <msup> <mover> <msub> <mi>F</mi> <mi>i</mi> </msub> <mo>&OverBar;</mo> </mover> <mi>s</mi> </msup> <mo>)</mo> </mrow> <mrow> <mi>f</mi> <mi>f</mi> </mrow> </msub> <mo>|</mo> </mrow> <mrow> <mn>2</mn> <mi>&beta;</mi> <mover> <mi>R</mi> <mo>&OverBar;</mo> </mover> </mrow> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>17</mn> <mo>)</mo> </mrow> </mrow>

Step 207：Time effect will be included in step 206Substitute into formula (18), it is determined that consider moment of flexure contribution because Son and mole-coulomb limited with stretching cut-off carefully see particle and bond season cracking criterion, and calculate j-th to k-th successively Rock mass carefully see particle two dimension bond stress, whether ruptured and fracture mode for judging that rock mass is carefully seen particle and bonded, at this The rock mass of criterion, which is carefully seen, contains power function type time effect and consideration moment of flexure contribution factor in particle bond stress,

<mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msup> <mi>f</mi> <mi>s</mi> </msup> <mo>=</mo> <msup> <mrow> <mo>(</mo> <msub> <mover> <mi>&tau;</mi> <mo>&OverBar;</mo> </mover> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>&prime;</mo> </msup> <mo>-</mo> <msub> <mover> <mi>&tau;</mi> <mo>&OverBar;</mo> </mover> <mi>c</mi> </msub> <mo>=</mo> <msup> <mrow> <mo>(</mo> <msub> <mover> <mi>&tau;</mi> <mo>&OverBar;</mo> </mover> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>&prime;</mo> </msup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <msub> <mover> <mi>&sigma;</mi> <mo>&OverBar;</mo> </mover> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>&prime;</mo> </msup> <mi>tan</mi> <mover> <mi>&phi;</mi> <mo>&OverBar;</mo> </mover> <mo>-</mo> <mover> <mi>c</mi> <mo>&OverBar;</mo> </mover> <mo>=</mo> <mfrac> <mrow> <mo>|</mo> <msup> <mover> <msub> <mi>F</mi> <mi>i</mi> </msub> <mo>&OverBar;</mo> </mover> <mi>s</mi> </msup> <mo>|</mo> </mrow> <mrow> <mn>2</mn> <mi>&beta;</mi> <mover> <mi>R</mi> <mo>&OverBar;</mo> </mover> </mrow> </mfrac> <mo>+</mo> <mfrac> <mn>1</mn> <mrow> <mn>2</mn> <mi>&beta;</mi> <mover> <mi>R</mi> <mo>&OverBar;</mo> </mover> </mrow> </mfrac> <mrow> <mo>(</mo> <mo>-</mo> <msup> <mover> <msub> <mi>F</mi> <mi>i</mi> </msub> <mo>&OverBar;</mo> </mover> <mi>n</mi> </msup> <mo>+</mo> <mfrac> <mrow> <mn>3</mn> <mover> <mi>&beta;</mi> <mo>&OverBar;</mo> </mover> <mo>|</mo> <msup> <mover> <msub> <mi>M</mi> <mi>i</mi> </msub> <mo>&OverBar;</mo> </mover> <mi>s</mi> </msup> <mo>|</mo> </mrow> <mrow> <mi>&beta;</mi> <mover> <mi>R</mi> <mo>&OverBar;</mo> </mover> </mrow> </mfrac> <mo>)</mo> </mrow> <mi>tan</mi> <mover> <mi>&phi;</mi> <mo>&OverBar;</mo> </mover> <mo>-</mo> <mover> <mi>c</mi> <mo>&OverBar;</mo> </mover> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msup> <mi>f</mi> <mi>n</mi> </msup> <mo>=</mo> <msup> <mrow> <mo>(</mo> <msub> <mover> <mi>&sigma;</mi> <mo>&OverBar;</mo> </mover> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>&prime;</mo> </msup> <mo>-</mo> <msub> <mover> <mi>&sigma;</mi> <mo>&OverBar;</mo> </mover> <mi>c</mi> </msub> <mo>=</mo> <mfrac> <mn>1</mn> <mrow> <mn>2</mn> <mi>&beta;</mi> <mover> <mi>R</mi> <mo>&OverBar;</mo> </mover> </mrow> </mfrac> <mrow> <mo>(</mo> <mo>-</mo> <msup> <mover> <msub> <mi>F</mi> <mi>i</mi> </msub> <mo>&OverBar;</mo> </mover> <mi>n</mi> </msup> <mo>+</mo> <mfrac> <mrow> <mn>3</mn> <mover> <mi>&beta;</mi> <mo>&OverBar;</mo> </mover> <mo>|</mo> <msup> <mover> <msub> <mi>M</mi> <mi>i</mi> </msub> <mo>&OverBar;</mo> </mover> <mi>s</mi> </msup> <mo>|</mo> </mrow> <mrow> <mi>&beta;</mi> <mover> <mi>R</mi> <mo>&OverBar;</mo> </mover> </mrow> </mfrac> <mo>)</mo> </mrow> <mo>-</mo> <msub> <mover> <mi>&sigma;</mi> <mo>&OverBar;</mo> </mover> <mi>c</mi> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>18</mn> <mo>)</mo> </mrow> </mrow>

Wherein：f^s、fⁿRespectively rock mass carefully sees timeliness shear fracture criterion, the timeliness tensile fracture criterion that particle two dimension bonds,Two dimension for the time effect of type containing power function of i-th of contact bonds shear stress,Contain power for i-th of contact Function type time effect and the two dimension bonding direct stress for considering moment of flexure contribution factor,Respectively rock mass carefully sees particle two Tensile strength, the shearing strength of bonding are tieed up,The cohesive strength that particle two dimension bonds carefully is seen for rock mass,Particle two is carefully seen for rock mass Tie up the internal friction angle of bonding；f^sParticle is carefully seen more than or equal to 0 expression rock mass and bonds shear fracture, and rock mass carefully sight is represented less than 0 Shear fracture does not occur for grain bonding；fⁿParticle is carefully seen more than or equal to 0 expression rock mass and bonds tensile fracture, represents that rock mass is thin less than 0 See particle and bond and tensile fracture does not occur；

Step 208：F in the formula (18) in step 207^sOr fⁿDuring more than or equal to 0, show that rock mass carefully sees particle and bonds hair Raw rupture, now rock mass carefully see the motor pattern of particle and expressed using the two-dimensional linear contact model of consideration damping effect；When The f in formula (18) in step 207^sAnd fⁿWhen both less than 0, show that rock mass is carefully seen particle and bonded and do not rupture, continue cycling through step 201 to 207, calculate, update, judging that rock mass carefully sees the bond state of particle contact, until rock mass does not produce new thin sight particle Bond rupture or rock mass carefully sees particle and bonds rupture accelerated development and form macroscopic failure, loop termination.

2. the thin construction method for seeing season cracking power function pattern type of rock mass two dimension according to claim 1, its feature exist In：The rock mass carefully sees the determination that particle two dimension bonds the initial time step size increments Δ t of timeliness decay deterioration, is to use to consider The thin sight particle of moment of flexure contribution factor bonds the two-dimentional power function pattern formula of timeliness deterioration decay, by the thin sight in each time step The decay first of particle two dimension bonding ruptures the time be lost to determine, i.e., presses power function type by first thin particle bonding of seeing Pattern carries out time divided by until the first thin calculating circulation time seen required for particle bonding ruptures that decay rupture is lasted Count to estimate initial time step size increments Δ t, see formulaIts In,Particle two dimension bonding diameter multiplier, n are carefully seen for the rock mass of i-th of contact_cFor first Rock mass carefully sees the number that particle two dimension bonds the cycle calculations needed for rupture, β_σ、β_τRespectively rock mass carefully sees particle two dimension and bonds drawing The timeliness deterioration factor corresponding to intensity, the timeliness deterioration factor corresponding to two-dimentional bond shear strength are stretched, i is followed successively by first to most The latter rock mass carefully sees particle and bonds number, and ∞ is infinity.

3. the thin construction method for seeing season cracking power function pattern type of rock mass two dimension according to claim 2, its feature exist In：The rock mass carefully sees particle two dimension and bonds timeliness deterioration factor-beta corresponding to tensile strength_σParticle two dimension is carefully seen with rock mass to bond Timeliness corresponding to shear strength deteriorates factor-beta_τDetermination comprise the following steps, the formula subscript 1 wherein included in these steps Represent first thin sight particle two dimension that timeliness decay deterioration is carried out by power function pattern formula and bond rupture label：

Step 211：Under two-dimensional case, speed, angular speed and given circulation that particle bonds both ends particle are carefully seen by rock mass Calculate time step increment Delta t_c, pass through formulaTurn it is determined that carefully seeing the relative of particle bonded contact AnglePass through formulaIt is determined that carefully seeing particle bonds normal direction incremental displacementIt is logical Cross formulaDetermine that particle bonds tangential incremental displacementPass through formulaDetermine the moment of flexure increment of particle bonded contact；

Step 213：Under two-dimensional case, pass through formulaIt is determined that carefully see the bonding of particle contact Direct stress, pass through formulaIt is determined that carefully see the bonding shear stress of particle contact, by A, I in the two formula andWith A', I' andReplace, then by formula (5) generation in the formula (6) and formula (7) and step 202 in step 203 Enter, obtain thin particle of seeing and bond comprising power function type time effect and consider that the two dimension of moment of flexure contribution factor bonds direct stress and calculated FormulaCalculation Shear formula is bonded with the two dimension comprising power function type time effect

4. the thin construction method for seeing season cracking power function pattern type of rock mass two dimension according to claim 1, its feature exist In：The rock mass is carefully seen after particle bonds and rupture, and rock mass carefully sees the motor pattern of particle using considering the two of damping effect Dimensional linear contact model is expressed, for describe rock mass carefully see particle bond the thin stress for seeing particle after season cracking, deformation and Moving law, consider that the structure of the two-dimensional linear contact model of damping effect comprises the following steps：

Step 301：By Monte Carlo searching algorithms, traversal find rock mass carefully see each two-dimensional linear contact jaw a of particle, Two-dimensional linear contact jaw b centre coordinate, under two-dimensional case, contact point a ends are calculated by formula (19), contact point b ends Centre distance：

Wherein：D is the centre distance between two-dimensional linear contact both ends particle and particle or particle and wall,For two dimension Linear contact end a coordinate,For two-dimensional linear contact jaw b coordinate；

Step 302：Rock mass is carefully seen the unit vector of each contact point between particle and calculated by formula (20) under two-dimensional plane state, If the contact between particle and particle, using obtained in step 301 two-dimensional linear contact both ends center point coordinate and away from From calculating；If particle contacts with wall, directly calculated using the normal vector equivalence replacement of wall；It is determined that each contact jaw Unit vector：

Wherein：n_iFor the unit vector of contact,For contact jaw b direction vector,For contact jaw a direction vector, n_wall To constrain the direction vector of wall；

Step 303：After rock mass carefully sees particle bonding rupture, the contact lap U of each two-dimensional linear contact point, pass through step 301 calculate the particle radius R at grain spacing d and two-dimensional linear contact both ends^a、R^b, recycle formula (21) to determine；Pass through Set particle two-dimensional linear contact reference distance g_r, and formula (22) is combined, determine the distance g of particle two-dimensional linear contact_s：

g_s=| U |-g_r (22)

Step 304：Determine that rock mass carefully sees grain contact point normal direction, tangential equivalent stiffness, using contact both ends particle entities or The rigidity k of wall^a, k^bThe equivalent rigidity instead of contact point, calculated by formula (23)：

Wherein：K_n、K_sGrain contact point equivalent normal stiffness and shear stiffness are carefully seen for rock mass, For particle and particle Or the normal stiffness and shear stiffness at contact a end of the particle with wall,For particle and particle or particle and wall Contact the normal stiffness and shear stiffness at b ends；

Step 305：Determine to contact the intergranular speed of related movement in both ends in rock mass, counted using formula (24), formula (25) Calculate；Wherein e_pqzFor RiccⁱIndex alternator, calculated according to formula (26)：

<mrow> <msub> <mi>V</mi> <mi>p</mi> </msub> <mo>=</mo> <msub> <mrow> <mo>(</mo> <msubsup> <mover> <mi>x</mi> <mo>&CenterDot;</mo> </mover> <mi>p</mi> <mrow> <mo>(</mo> <mi>c</mi> <mo>)</mo> </mrow> </msubsup> <mo>)</mo> </mrow> <mi>b</mi> </msub> <mo>-</mo> <msub> <mrow> <mo>(</mo> <msubsup> <mover> <mi>x</mi> <mo>&CenterDot;</mo> </mover> <mi>p</mi> <mrow> <mo>(</mo> <mi>c</mi> <mo>)</mo> </mrow> </msubsup> <mo>)</mo> </mrow> <mi>a</mi> </msub> <mo>=</mo> <mrow> <mo>(</mo> <msubsup> <mover> <mi>x</mi> <mo>&CenterDot;</mo> </mover> <mi>p</mi> <mrow> <mo>(</mo> <mi>b</mi> <mo>)</mo> </mrow> </msubsup> <mo>+</mo> <msub> <mi>e</mi> <mrow> <mi>p</mi> <mi>q</mi> <mi>z</mi> </mrow> </msub> <msubsup> <mi>&omega;</mi> <mi>q</mi> <mrow> <mo>(</mo> <mi>b</mi> <mo>)</mo> </mrow> </msubsup> <mo>(</mo> <mrow> <msubsup> <mi>x</mi> <mi>z</mi> <mrow> <mo>(</mo> <mi>c</mi> <mo>)</mo> </mrow> </msubsup> <mo>-</mo> <msubsup> <mi>x</mi> <mi>z</mi> <mrow> <mo>(</mo> <mi>b</mi> <mo>)</mo> </mrow> </msubsup> </mrow> <mo>)</mo> <mo>)</mo> </mrow> <mo>-</mo> <mrow> <mo>(</mo> <msubsup> <mover> <mi>x</mi> <mo>&CenterDot;</mo> </mover> <mi>p</mi> <mrow> <mo>(</mo> <mi>a</mi> <mo>)</mo> </mrow> </msubsup> <mo>+</mo> <msub> <mi>e</mi> <mrow> <mi>p</mi> <mi>q</mi> <mi>z</mi> </mrow> </msub> <msubsup> <mi>&omega;</mi> <mi>q</mi> <mrow> <mo>(</mo> <mi>a</mi> <mo>)</mo> </mrow> </msubsup> <mo>(</mo> <mrow> <msubsup> <mi>x</mi> <mi>z</mi> <mrow> <mo>(</mo> <mi>c</mi> <mo>)</mo> </mrow> </msubsup> <mo>-</mo> <msubsup> <mi>x</mi> <mi>z</mi> <mrow> <mo>(</mo> <mi>a</mi> <mo>)</mo> </mrow> </msubsup> </mrow> <mo>)</mo> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>24</mn> <mo>)</mo> </mrow> </mrow>

<mrow> <msub> <mi>V</mi> <mi>q</mi> </msub> <mo>=</mo> <msub> <mrow> <mo>(</mo> <msubsup> <mover> <mi>x</mi> <mo>&CenterDot;</mo> </mover> <mi>q</mi> <mrow> <mo>(</mo> <mi>c</mi> <mo>)</mo> </mrow> </msubsup> <mo>)</mo> </mrow> <mi>b</mi> </msub> <mo>-</mo> <msub> <mrow> <mo>(</mo> <msubsup> <mover> <mi>x</mi> <mo>&CenterDot;</mo> </mover> <mi>q</mi> <mrow> <mo>(</mo> <mi>c</mi> <mo>)</mo> </mrow> </msubsup> <mo>)</mo> </mrow> <mi>a</mi> </msub> <mo>=</mo> <mrow> <mo>(</mo> <msubsup> <mover> <mi>x</mi> <mo>&CenterDot;</mo> </mover> <mi>q</mi> <mrow> <mo>(</mo> <mi>b</mi> <mo>)</mo> </mrow> </msubsup> <mo>+</mo> <msub> <mi>e</mi> <mrow> <mi>p</mi> <mi>q</mi> <mi>z</mi> </mrow> </msub> <msubsup> <mi>&omega;</mi> <mi>p</mi> <mrow> <mo>(</mo> <mi>b</mi> <mo>)</mo> </mrow> </msubsup> <mo>(</mo> <mrow> <msubsup> <mi>x</mi> <mi>z</mi> <mrow> <mo>(</mo> <mi>c</mi> <mo>)</mo> </mrow> </msubsup> <mo>-</mo> <msubsup> <mi>x</mi> <mi>z</mi> <mrow> <mo>(</mo> <mi>b</mi> <mo>)</mo> </mrow> </msubsup> </mrow> <mo>)</mo> <mo>)</mo> </mrow> <mo>-</mo> <mrow> <mo>(</mo> <msubsup> <mover> <mi>x</mi> <mo>&CenterDot;</mo> </mover> <mi>q</mi> <mrow> <mo>(</mo> <mi>a</mi> <mo>)</mo> </mrow> </msubsup> <mo>+</mo> <msub> <mi>e</mi> <mrow> <mi>q</mi> <mi>p</mi> <mi>z</mi> </mrow> </msub> <msubsup> <mi>&omega;</mi> <mi>p</mi> <mrow> <mo>(</mo> <mi>a</mi> <mo>)</mo> </mrow> </msubsup> <mo>(</mo> <mrow> <msubsup> <mi>x</mi> <mi>z</mi> <mrow> <mo>(</mo> <mi>c</mi> <mo>)</mo> </mrow> </msubsup> <mo>-</mo> <msubsup> <mi>x</mi> <mi>z</mi> <mrow> <mo>(</mo> <mi>a</mi> <mo>)</mo> </mrow> </msubsup> </mrow> <mo>)</mo> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>25</mn> <mo>)</mo> </mrow> </mrow>

Wherein：V_pWith V_qEquivalence, V_pWith V_qTo contact the intergranular speed of related movement in both ends in rock mass, p, q are index symbol of equal value Number, p=1, q=1 represent that particle contacts with particle, and expression particle contacts with wall when p=2, q=2,For particle With the speed of the contact b end units of particle or particle with wall,It is particle and particle or particle and wall The speed of a end units is contacted,It is angular speed of the particle with the contact a end units of particle or particle with wall,It is angular speed of the particle with the contact b end units of particle or particle with wall,Be particle with particle or The displacement at contact a end of the grain with wall,It is displacement of the particle with the contact b ends of particle or particle with wall,For drift index The middle transition symbol of conversion,The speed at the contact a ends of pellet-pellet or particle-wall when index symbol is p is represented,The speed at the contact a ends of pellet-pellet or particle-wall when index symbol is q is represented,When expression index symbol is p The speed at the contact b ends of pellet-pellet or particle-wall,Represent pellet-pellet or particle-wall when index symbol is q Contact b ends speed, only a ends and two, b ends contact jaw；

Step 306：For the thin initial time step size increments Δ t for seeing particle linear contact model of rock mass value, pass through formula (29) the minimum time step Δ t of estimation, it is ensured that the calculating time step of constructed model is less than the value, you can ensure system product Calculating is divided to tend towards stability；The total displacement increment of each linear contact, method are determined by formula (30), formula (31), formula (32) To displacement increment and tangential displacement increment：

R=min (R_a,R_b) (27)

ΔU_p1=V_p1Δt (30)

<mrow> <msub> <mi>&Delta;&delta;</mi> <mi>n</mi> </msub> <mo>=</mo> <msubsup> <mi>&Delta;U</mi> <mrow> <mi>p</mi> <mn>1</mn> </mrow> <mrow> <mi>n</mi> <mi>l</mi> </mrow> </msubsup> <mo>=</mo> <msub> <mi>V</mi> <mrow> <mi>q</mi> <mn>1</mn> </mrow> </msub> <msub> <mi>n</mi> <mrow> <mi>q</mi> <mn>1</mn> </mrow> </msub> <msub> <mi>n</mi> <mrow> <mi>p</mi> <mn>1</mn> </mrow> </msub> <mi>&Delta;</mi> <mi>t</mi> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>31</mn> <mo>)</mo> </mrow> </mrow>

<mrow> <msub> <mi>&Delta;&delta;</mi> <mi>s</mi> </msub> <mo>=</mo> <msubsup> <mi>&Delta;U</mi> <mrow> <mi>p</mi> <mn>1</mn> </mrow> <mrow> <mi>s</mi> <mi>l</mi> </mrow> </msubsup> <mo>=</mo> <msub> <mi>&Delta;U</mi> <mrow> <mi>p</mi> <mn>1</mn> </mrow> </msub> <mo>-</mo> <msubsup> <mi>&Delta;U</mi> <mrow> <mi>p</mi> <mn>1</mn> </mrow> <mrow> <mi>n</mi> <mi>l</mi> </mrow> </msubsup> <mo>=</mo> <msub> <mi>V</mi> <mrow> <mi>p</mi> <mn>1</mn> </mrow> </msub> <mi>&Delta;</mi> <mi>t</mi> <mo>-</mo> <msub> <mi>V</mi> <mrow> <mi>q</mi> <mn>1</mn> </mrow> </msub> <msub> <mi>n</mi> <mrow> <mi>q</mi> <mn>1</mn> </mrow> </msub> <msub> <mi>n</mi> <mrow> <mi>p</mi> <mn>1</mn> </mrow> </msub> <mi>&Delta;</mi> <mi>t</mi> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>32</mn> <mo>)</mo> </mrow> </mrow>

Wherein：R is the equivalent redius that rock mass carefully sees particle, and m is that rock mass carefully sees granular mass, and J1 is the rotation that rock mass carefully sees particle Inertia；k^{It is flat}Particle system translational stiffness, k are carefully seen for rock mass^TurnParticle system rotational stiffness is carefully seen for rock mass；ΔU_p1Carefully seen for rock mass The total displacement increment of particle two-dimensional linear contact, Δ δ_n、Physical significance is identical, represents that rock mass carefully sees particle two-dimensional linear The Normal Displacement increment of contact, Δ δ_s、Physical significance is identical, represents that rock mass carefully sees cutting for particle two-dimensional linear contact To displacement increment, V_p1With V_q1The speed of related movement at particle contact both ends is carefully seen for rock mass, n is unit normal vector, and p1, q1 are Tensor index figure shift；

Step 307：The ultimate range as existing for formula (22) judgement rock mass carefully sees particle surface contact permission, calculates normal direction and cuts To displacement updating factor, in addition, rock mass carefully sees the renewal of particle two-dimensional linear contact normal direction displacement increment using back The product of Normal Displacement increment and updating factor α obtains, and rock mass carefully sees the renewal of particle two-dimensional linear contact tangential displacement increment It is to be obtained using the tangential displacement increment of back and updating factor α product；

<mrow> <mi>&alpha;</mi> <mo>=</mo> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <mfrac> <msub> <mi>g</mi> <mi>s</mi> </msub> <mrow> <msub> <mi>g</mi> <mi>s</mi> </msub> <mo>-</mo> <msub> <mrow> <mo>(</mo> <msub> <mi>g</mi> <mi>s</mi> </msub> <mo>)</mo> </mrow> <mn>0</mn> </msub> </mrow> </mfrac> <mo>,</mo> <msub> <mrow> <mo>(</mo> <msub> <mi>g</mi> <mi>s</mi> </msub> <mo>)</mo> </mrow> <mn>0</mn> </msub> <mo>></mo> <mn>0</mn> <mo>,</mo> <msub> <mi>g</mi> <mi>s</mi> </msub> <mo><</mo> <mn>0</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mn>1</mn> <mo>,</mo> <mi>o</mi> <mi>t</mi> <mi>h</mi> <mi>e</mi> <mi>r</mi> <mi>w</mi> <mi>i</mi> <mi>s</mi> <mi>e</mi> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>33</mn> <mo>)</mo> </mrow> </mrow>

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 308：The normal direction linear force that rock mass carefully sees the contact of particle two-dimensional linear takes relative vector to add up M_l=1 swears with absolute The cumulative M of amount_l=0 pattern, calculated and obtained by formula (33), (34)；Rock mass carefully sees the tangential linear of particle two-dimensional linear contact Power carefully sees particle contact slide using rock mass to represent, is calculated and obtained by formula (35)：

<mrow> <msubsup> <mi>F</mi> <mi>n</mi> <mi>l</mi> </msubsup> <mo>=</mo> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>k</mi> <mi>n</mi> </msub> <msub> <mi>g</mi> <mi>s</mi> </msub> <mo>,</mo> <msub> <mi>g</mi> <mi>s</mi> </msub> <mo>&le;</mo> <mn>0</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mn>0</mn> <mo>,</mo> <mi>o</mi> <mi>t</mi> <mi>h</mi> <mi>e</mi> <mi>r</mi> <mi>w</mi> <mi>l</mi> <mi>s</mi> <mi>e</mi> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> <msub> <mi>M</mi> <mi>l</mi> </msub> <mo>=</mo> <mn>0</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>m</mi> <mi>i</mi> <mi>n</mi> <mrow> <mo>(</mo> <msub> <mrow> <mo>(</mo> <msubsup> <mi>F</mi> <mi>n</mi> <mi>l</mi> </msubsup> <mo>)</mo> </mrow> <mi>o</mi> </msub> <mo>+</mo> <msub> <mi>k</mi> <mi>n</mi> </msub> <msub> <mi>&Delta;&delta;</mi> <mi>n</mi> </msub> <mo>,</mo> <mn>0</mn> <mo>)</mo> </mrow> <mo>,</mo> <msub> <mi>M</mi> <mi>l</mi> </msub> <mo>=</mo> <mn>1</mn> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>33</mn> <mo>)</mo> </mrow> </mrow>

<mrow> <msubsup> <mi>F</mi> <mi>s</mi> <mo>*</mo> </msubsup> <mo>=</mo> <msub> <mrow> <mo>(</mo> <msubsup> <mi>F</mi> <mi>s</mi> <mi>l</mi> </msubsup> <mo>)</mo> </mrow> <mi>o</mi> </msub> <mo>-</mo> <msub> <mi>k</mi> <mi>s</mi> </msub> <msub> <mi>&Delta;&delta;</mi> <mi>s</mi> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>34</mn> <mo>)</mo> </mrow> </mrow>

Wherein：Respectively rock mass carefully sees the two-dimensional linear contact normal direction linear force, tangential linear of stress deformation between particle Power, k_n、k_sRespectively rock mass carefully sees the two-dimensional linear contact normal direction of stress deformation between particle, tangential linear rigidity, Δ δ_n、Δδ_s Respectively rock mass carefully sees the Normal Displacement increment of particle two-dimensional linear contact, tangential displacement increment,Respectively rock Body carefully sees the initial normal force increment size of particle two-dimensional linear contact, tangential force increment size,Particle is carefully seen for rock mass not slide When stiction,Particle force of sliding friction is carefully seen for rock mass, its value can by friction coefficient μ withProduct obtains；

Step 309：The normal direction damping that rock mass carefully sees particle linear contact uses full normal mode M_d={ 0,2 } and tensionless winkler foundation pattern M_dTwo kinds of={ 1,3 }, calculated by formula (36), wherein m_cFor equivalent particle quality, calculated by formula (37), rock mass carefully sight The tangential damping of grain linear contact uses full shear mode M_d={ 0,1 } and cunning-cut-off-die formula M_d={ 2,3 }, come according to formula (38) Calculate,

<mrow> <msubsup> <mi>F</mi> <mi>n</mi> <mi>d</mi> </msubsup> <mo>=</mo> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <mo>(</mo> <mn>2</mn> <msub> <mi>&beta;</mi> <mi>n</mi> </msub> <msqrt> <mrow> <msub> <mi>m</mi> <mi>c</mi> </msub> <msub> <mi>k</mi> <mi>n</mi> </msub> </mrow> </msqrt> <mo>)</mo> <msub> <mover> <mi>&delta;</mi> <mo>&CenterDot;</mo> </mover> <mi>n</mi> </msub> <mo>,</mo> <msub> <mi>M</mi> <mi>d</mi> </msub> <mo>=</mo> <mo>{</mo> <mn>0</mn> <mo>,</mo> <mn>2</mn> <mo>}</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>m</mi> <mi>i</mi> <mi>n</mi> <mrow> <mo>(</mo> <msup> <mi>F</mi> <mo>*</mo> </msup> <mo>,</mo> <mo>-</mo> <msubsup> <mi>F</mi> <mi>n</mi> <mi>l</mi> </msubsup> <mo>)</mo> </mrow> <mo>,</mo> <msub> <mi>M</mi> <mi>d</mi> </msub> <mo>=</mo> <mo>{</mo> <mn>1</mn> <mo>,</mo> <mn>3</mn> <mo>}</mo> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>36</mn> <mo>)</mo> </mrow> </mrow>

<mrow> <msubsup> <mi>F</mi> <mi>s</mi> <mi>d</mi> </msubsup> <mo>=</mo> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <mo>(</mo> <mn>2</mn> <msub> <mi>&beta;</mi> <mi>s</mi> </msub> <msqrt> <mrow> <msub> <mi>m</mi> <mi>c</mi> </msub> <msub> <mi>k</mi> <mi>s</mi> </msub> </mrow> </msqrt> <mo>)</mo> <msub> <mover> <mi>&delta;</mi> <mo>&CenterDot;</mo> </mover> <mi>s</mi> </msub> <mo>,</mo> <msub> <mi>M</mi> <mi>d</mi> </msub> <mo>=</mo> <mo>{</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mo>}</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mn>0</mn> <mo>,</mo> <msub> <mi>M</mi> <mi>d</mi> </msub> <mo>=</mo> <mo>{</mo> <mn>2</mn> <mo>,</mo> <mn>3</mn> <mo>}</mo> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>38</mn> <mo>)</mo> </mrow> </mrow>

Wherein：Respectively rock mass carefully sees the linear damping force of normal direction of particle linear contact, tangential linear damping power, β_n The normal direction damped coefficient of particle linear contact, β are carefully seen for rock mass_sThe tangential damped coefficient of particle linear contact, k are carefully seen for rock mass_n The normal direction linear rigidity of particle linear contact, k are carefully seen for rock mass_sThe tangential linear rigidity of particle linear contact is carefully seen for rock mass,Respectively rock mass carefully sees the normal direction speed and tangential velocity of particle linear contact, F^*Particle is carefully seen for rock mass linearly to connect Tactile full normal direction damping force, expression formula areM c are that rock mass carefully sees equivalent particle quality, m⁽¹⁾For rock mass The thin thin sight granular mass for seeing particle contact jaw 1, m⁽²⁾The thin sight granular mass of particle contact jaw 2, F are carefully seen for rock mass^dFor rock mass The thin total damping power for seeing particle linear contact.