RMZ – MATERIALI IN GEOOKOLJE

thrмR iλ = 2 λ= 100⋅exp[ −( 3 k ⋅ k+0.01 ⋅0.05)D ] 3i ,% Ah + 2+qR ⋅ CnU = K[ 3 Q / R]p⋅ρ1− µ406 nShemetov, P. A., Bibik, I. P.H U K[ 3уCtg=+ CQb/ R]D =Кk αW W .U0.667 0.5µх1 0λ = =n = 2− ≥ F3 1.05 D ( s )( k +f0.05) KeD+avewhere U – ave µ2+V V1− µ( s)1 0velocity of rock displacementcaused 1−µ by explosion (cm/s); U oRupture (breaking) σn = 2 −adm .= ρstress ⋅ С р⋅Ucan adm. be definedas follows:– 55 safe velocity of rock displacementnU 0.667U0.50.35 admK[ 3.≥ U х4/34K k = Q / R]f= λ = 1based on, + k =⎡⎤1.05+Dconditions of their nUelastic deformationadm(20).≥ UU х K[ (cm/s).31,05+D 3 ⎛ V0⎞ ⎛ V0⎞4 0.1σ= k + 0.05avet( s )3≥ Kt ⋅lg R,c( s )Daveave ( s)Q / R]Dcomave ( s)σ ⎢⎜⎟⎜⎟р= −К − ⎥adm .=µ8ρ ⋅ С р⋅U ⎢⎣⎝ V adm.1 ⎠ ⎝ V1⎠ ⎥6 ⎦0,4n = 2 −Q Velocity σ of rock displacement U dependingon charge 1−1,05where K – coefficient depending onadm0.667.= ρ ⋅ С р⋅U adm.µn =q2( 0.4sin2 10.353.72 ⋅10⋅ Q− −αVµc+ 0.65)( 0.5 − 0.016m)λ = K1+ KBE thr= k =U =properties of massif.1.75µ+ Dsize, distances3Q k + 0.05toV0.01 avet( s )σ3 ≥ K1 + σt ⋅lg R,cD Ah + q2 + σ R ⋅ C3p⋅ ρ0ave ( s)protected object U and elastic impedancet Stress on elementary surface insideof 3≥rock Kt can⋅lgbeR,admc.≥ U хЕ6 0,4U expressed by the follow-formula: уCtgα+ Cadm .≥ U∆ Hхthe rigid body acts on both normal andaing3.72 ⋅10⋅ Qq( 0.4sin2αc+ 0.65b)( 0.5 − 0.016m)U = W1 W0K K=8/3∆ thr= D =1.75σ60,4tangent. The body referred to three perpendicularaxes Q x3.72 ⋅10adm .= ρ ⋅ С⋅ Qр⋅U adm.3 {[ 1−+ ( 1−2≥μF3) ⋅ ε]−1}∆r6m) U = σК0.013f adm(18), Q у, Q zis affected.=K Ah + qR ⋅ Cρ ⋅ С р⋅U σ р = − ⋅ КVp⋅ ρe⋅ 1V0adm.8.351.75[ 1+( 1−2μ)⋅ ε] 4R ⋅ Cnρby at least three stress components s 1,U = K[ 3 Q / R]p⋅5+ave ( s )HQt3 ≥ Kt ⋅lg R,cswhereуCtgα+ CQ –bweight of simultaneously 2, s 3causing 6 more components s ху,a(sd ) = , m 55W1 W04/34D = t sblasted charge (kg); R – distance to уz. s xz, s ухand etc. Action of theseave( s )3≥ Kt ⋅lg R,cqHK U ⋅ С ρf= ,− ≥ Fруvery components of stress causes deformationof volume Vprotected W1 Wµσ =3 ⎡⎛V⎤0⎞ ⎛ V ⎞К30fK 4n = 2 −0.1σVe6 0,41V0σ ⎢com0−objected≥ F 3.72 (m); ⋅10C p⋅ Q r – elastic q⎜⎟⎜⎟р= − ⋅ К − ⎥8)( 0.5 − 0. 016m1) − µ⎢impedance ofUrock = 6 0,4(m/s kg/m 3 ).0⎣to ⎝ V1⎠1during ⎝ V1its ⎠ ⎥⎦V1V 3.72 1.750+ qR⋅10⋅⋅ Q.5 − 0. 016mCp⋅ ρ change from r 0to r 1.1.13 55 Q )VHUq=4/341.758/3q β = Karctgf= =USafe adm .≥velocity U, KBE ,deg Rх of rockree;⋅ Cdisplacement p⋅ ρ12,5 3 ⎡⋅⎛Ср⋅{ [ 1( 1−2μ)⋅εo] −1} ⋅(1+QdcaneγUGiven = σV⎤0Vo1 +⎞σ 2 +⎛σV0⎞4 0.1σσthat⎢30com⎜in whole definesvolumetric strain (relative vol-be determined ⎡ from 4/3 general 4conditions⎤of their 3 Wdeformation.⎛ V1 0⎞ W[ 1⎟+ ( 1−⎜2μ⎟р= − ⋅ К − ⎥48 ⎢0⎢ If⎛in V0the⎞⎣⎝V1⎠ Е ⎝ V1⎠)⋅⎥⎦εo] ⋅( 1− µ )σ = −− ⎥course ofadmdeformation ⎜⎢ of volume ⎟⎜⎟р .= ρ ⋅WКС р⋅U adm.− ≥ FQ8 1oto ⎥ volume ume deformation) (e) of the medium⎣⎝VWV∆=a0K π K⋅γ = −11 ⎠ V≥0 F⎝V1⎠8/3BE ∆d⎦0.2282.28Q 2eV 1the specific − 2V∆c1energy V0of volume V oin-K by some R c final and quite definite s 2under σ action 1380⋅Qof total ⋅3[ 1stress + ( 1−{ [ 12μ+tensor )( 1⋅ε−2]μ)⋅ ε]o (s 1, ⎛1−1}Vqr1 + σ 2 + σ3R = σ р = − ⋅ К ⋅0⋅⎜Н = tcreases , s 3), we obtain:3≥t⋅lg , m,0.856 0.2863for σ21 ⋅ ctg + certain σ 2 α + σ4/34CЕ8{[ ( ) [ 1+] ( } 8 / 1−2 0. μ 57 ) ⋅ ε1 1 2μ εo1 ⎝] ρ + − ⋅14+medium 3 3value ⎡⎛F, V this ⎞ forms ⎛ ⎞ ⎤ p∆ Q0V0necessary aЕ and σ6= sufficient −0,4⋅ ⎢ conditions − ⎥6m) for rupture. 3.72 ⋅10Then, ⋅ Q⎜⎟⎜⎟р ⎡ К4/34K = ad = 3,m⎤U =general 8 ⎛ V ⎞⎢ ⎢0⎣⎝V ⎛ V0⎞U ⋅ С ρ8/3∆σ = − ⋅ equation 1 ⎠−⎝ V 3qH{[ 1+( 1−2μ)⋅рε]−1}∆rof 1⎥⎠⎥⎦(21)energy 1.75⎜⎟⎜⎟р у КσbastbastΣ р ( B=−+P⋅К)σ⋅=σRconditions defining 8/3 potential3 ⋅ C 8{[ 1p+ ⋅ ρ ⎢⎥( 1⎣⎝ V1⎠ ⎝ Vn ntσt1D = 2 2⎠ 8дD−12μ)⋅ ε]−} ⎦= 6,5 [ 1+( 1−q2μ)⋅ ε] 40− +σrupture hrр = − of ⋅ Кmedium hrσ ⋅ can be presented astfollows: 8 σ1 + σnQta1.13[ σ1H2+ + ( 1σq−3 2μ)⋅ ε] 4 where-1,8Е – dynamic modulus of elasticity;8/d= , mU ⋅ Сβ = arctgW W σ1 + σ 2 + Еσ,deg ree;3Lр ρ 12,5 ⋅С⋅STEM{[ 1+( 1−2μ)⋅ε]qHрos 1, s 2, s 3– total stress tensor;negativenу1 0 deγσ = Uo=4−(19)l U ⋅ С≥FЕρqvalues of s рconform∑[ 1+( 1−2μ)⋅εo] ⋅(1опрσVi1=V0to 8/3i=1 3compression stress as in this casel (where W 0and {[ 1+( 1−2μ)⋅ ε]−1}д= − 1.5...5. 0σ) dadhole р W=1−д– energy ⋅ К ⋅ of medium 8/3n1.13Hq π ⋅3γdeformations are positive, and positiveεbefore and 2 after rupture 8 {[ 1+( 1(kg m); [ 1−+2μV( 1)−⋅ ε0and 2]μ)⋅− 1] }σdК48/3β = arctg ,deg ree0.228рe = − ⋅−2;12,5 ⋅Сcр⋅{ [ 1+( 1−2μ)⋅εo⋅values of s 1380рconform ⋅Qto ⋅[ ] −1tensile 1+(} ⋅( 1+μ1−2μ)⋅ε])d4/34V 1– volume ⎡ qН 12,5 = ⋅⎛of medium⋅{ [ 1+( 1−before ⎤2μ)⋅εand 8/33 СV8⎞⎛ ⎞ ]afterrupture (m 3 р−1} stress⋅( 1+μas )deformations are negative0, Vm[ 1+( 1−2μ)⋅ ε] 4oeγUo=R =4[ 1+( 0.856 1−2μ0.286) ⋅εo30σoU = − ⋅ ⎢ ). − ⎥ here.o⎜⎟⎜⎟рКC ρ {[ ] ⋅( 1− µ )1+( 1−2μ)⋅ε]8 /2 ⋅ ctgUαo−⋅ С ρp8 ⎢4⎣⎝σV[ 1 + ⎠ ( 1−⎝2μVрπ ⋅γU=⋅ С ρ1)⎠⋅ε⎥⎦o] ⋅( 1− µ )р0.2282.280.2dσ c=qe− 21380⋅Q⋅[ 1+RMZ-M&G( 1−2μ)⋅ε2012, o]59⎛1−µ ⎞qbastqbast R = Σ(Bn+ Pn)⋅⎜⎟Н =σtσ0.57tσ σ σ 0.2282.280.57= 6,51 + D д 2=+ D,032m0.856 0.2863− 2 + 1 C ρ {[ 1+( 1−2μ)⋅ε] }8 / 18/3o−1⎝ + µp⎠2 ⋅ ctgαU adm≥nμµµ2.21