Investigation of a ydaulic imact a tecnology in ock beaking Matin Genet * Laboatoie de Mécanique et de Tecnologie, 61 av. du Pésident Wilson, 94235 Cacan Cedex, Fance D. Wenyi Yan Senio Lectue Deatment of Mecanical Engineeing Building 31, Monas Univesity, VIC800, Austalia P. Tan Tan-Cong RME Cai in Comutational Engineeing, Comutational Engineeing and Science Reseac Cente, Univesity of Souten Queensland, Toooomba, Austalia *Coesonding auto. Tel: 0033147402225, E-mail: matin.genet@lmt.ens-cacan.f Submitted to Acive of Alied Mecanics
Abstact Te finite element metod and dimensional analysis ave been alied in te esent ae to study a ydaulic imact, ic is utilized in a non-exlosive ock beaking tecnology in mining industy. Te imact ocess of a ig seed iston on liquid ate, eviously intoduced in a boeole dilled in ock, is numeically simulated. Te eseac is focused on te influences of all te aametes involved in te tecnology on te lagest incial stess in te ock, ic is consideed as one of te key factos to beak te ock. Ou detailed aametic investigation eveals tat te vaiation of te isotoic ock mateial oeties, esecially its density, as no significant influence on te lagest incial stess. Te influences of te det of te ole and te det of te ate column ae also vey small. On te ote and, inceasing te initial kinetic enegy of te iston can damatically incease te lagest incial stess and te best ay to incease te initial kinetic enegy of te iston is to incease its initial velocity. Results fom te cuent dimensional analysis can be alied to otimize tis non-exlosive ock beaking tecnology. Key ods Finite element simulation, Dimensional analysis, Rock beaking, Non-exlosive metod, Hydaulic imact. 1 Intoduction Exlosives ae commonly used to fagment lage ock masses in moden mining actice. Fom te tecnical oint of vie, altoug exlosive metod is oeful, it does not oduce fagments it omogeneous size distibution. In many situations te amount of vey fine ocks is ig, ile in ote situations te amount of ovesized bouldes could be excessive. Futemoe, exlosive metod involves comlex dilling, blasting, scaling, gound suot and te evacuation of eole and equiment befoe blasting. Suc a multi-activity cycle is 2
time-consuming, inefficient and unoductively exensive [1]. Anote majo concen it exlosive blasting is te associated dange and undesiable imact on te envionment suc as fly ocks, ai blast, noise ollution and toxic fumes. Wen blasting occus close to esidential aeas, o duing tunnel constuction, envionmental otection egulation could seiously affect te ate of ock excavation. In some cases, blasting ould be excluded as an accetable metod of ock beaking. Aat fom te beaking of lage ock masses fo tansotability uoses, tunnelling equies moe caefully contolled ock beaking. Ovesized bouldes often cause blockage of mine da oints. Wen suc blockage occus, extensive sutdon of mine oeation ill esult, causing loss of millions of dollas e ou. Tus, fast, simle, safe and clean metods of beaking bouldes ae equied in some cases to make total mining oeation efficient. To ovecome te dabacks of exlosive metods, seveal non-exlosive tecnologies ave been develoed in te ast, see Sing [1]. Young [2] ovided an ovevie and comaed te os and cons of vaious metods of essuising a boeole in a ock mass, including small cage exlosive and oellant, ate jets, fiing of ig seed ate slugs, mecanical slittes, and ig essue gases. McCaty [3] oosed te use of oellant catidge in a edilled ole to ovide te beaking foce. In te latest atent by Young [4], a igessue foam as utilized to elace exlosive tecnology. Te contolled-foam injection (CFI) metod invented by Young [1, 4] as a numbe of advantages, including loe maximum essue and te maintenance of essue duing factue by vitue of te comessibility of te foam. Anote non-exlosive ock beaking metod as invented and atented by Denisat et al. [5], ic is illustated in Fig. 1. Te ydaulic fluid, suc as ate, is intoduced in a e-dilled boeole and is imulsively loaded by a ig seed iston. Te igly essuized ate, it te eflection of te essue ave, ill esult in 3
uge stesses in te ock mass, esecially at te bottom of te ole, ic is a stess aise. Consequently, cacks ill be initiated aound te boeole, esecially at te bottom, and te essuized ate ill enetate into te cacks, oviding te diving foce fo cack oagation. Eventually, cacks ill oagate back to te suface due to fee suface effect and a volume of te ad mateial ill be emoved. All te available inventions and atents focused on te incile of te ock beaking metods, i.e., diffeent aoaces ae used to anse te basic question of o to beak a ock mass. In tems of te alication of te non-exlosive tecnology, e need to quantify many aametes, suc as te det of te boeole and te initial velocity of te iston, etc. In te cuent investigation, te dimensional analysis and numeical metod ae alied to quantify te ydaulic imact ocess, ic is involved in a non-exlosive ock beaking tecnology as son in Fig. 1. Te efficiency of te imact is evaluated by te maximum incial stess in te ock duing an imact ocess. Numeical esults fom te investigation ill assist industy to quantitatively aly tis non-exlosive ock beaking tecnology and, teefoe, to imove ock beaking efficiency. Tis ae is stuctued as follos. Te finite element model to simulate te ydaulic imact is esented in Section 2. Te functional elationsi beteen te lagest incial stess in te ock and all te ocessing aametes fom dimensional analysis is discussed in Section 3. In Section 4, detailed numeical esults on te influences of all te aametes on te lagest incial stess ae discussed. Finally, conclusions ae given in Section 5. 2 Imact simulation 2.1 Finite element mes 4
Te finite element metod as been alied to simulate te ydaulic imact ocess. We use a finite element ackage, CASTEM, to ceate te finite element mes, a PERL scit to tanslate CASTEM meses into ABAQUS meses, te commecial ackage ABAQUS/Exlicit to do te simulations, and a PYTHON scit to automate te simulation ocess. Te boeole, as son in Fig. 1, can be idealized as a cylinde. Teefoe, tis oblem can be teated as axisymmetic. Moeove, te ock body can be consideed as semi-infinite. Infinite elements ae utilized to simulate te semi-infinite body. Fig. 2 sos te finite element mes geneated by using CASTEM. Te definition of te geometical aametes son in Fig.2 can also be found in Table 1. As son in Fig. 2, tee is an ac it te adius of R at te bottom of te boeole. Te eason to intoduce te ac is to avoid singulaity, ic imlies an infinite stess. Moeove, it is a good eesentation of te eality. It is imossible to ave a efect igt angle actically en e dill a ole and e alays ave te tace of te tool on te macined at. Fute exlanation of tis assumtion can be found in Section 3. a As son in Fig. 2, vey fine meses ae geneated aound te cone of te bottom of te ole. Many simulation tests it diffeent mes densities ave been caied out to eliminate te influence of mes density and detemine te final mes fo te calculations. In te end, tee ae 122 fou-node bilinea elements and 4349 tee-node linea elements in te final model. Te only initial condition in tis oblem is te initial velocity of te iston, ic is an additional aamete of te oblem. 5
2.2 Mateial oeties Te iston is nomally made of steel, ic is assumed to be a omogeneous and isotoic mateial. We also assume tat te iston stays in its elastic domain duing te imact ocess. Tus e can coose te iston s mateial data as Young s modulus E = 200 GPa, Poisson's atio! = 0.3 and density 3! = 7800 Kg / m. Duing te tansient imact ocess, te ate in te boeole can be consideed as still, i.e., no flo. Accoding to Wilson [6], e can model te ate as an elastic, omogeneous and isotoic solid it teses mateial data: Young s modulus E = 6207813 Pa, Poisson's atio! = 0.4995 and density 3! = 1000 Kg / m. In te cuent investigation, te ock in tis simulation is simlified as an elastic, omogeneous and isotoic solid. In eality, ock, as a natual mateial, consists of cystal, gains, cementitious mateials, voids, oes and flas, see [7]. At te fist stage of investigating tis non-exlosive ock beaking tecnology, ou cuent objective is to undestand and quantify te imact ocess. Consideing te influence of te inomogeneous micostuctue of ock mateial ill be ou next task. On te ote and, because of te uncetainty of te micostuctue and its inomogeneity, te assumed isotoic ock in ou model can be teated as a eesentative of te eal mateial and te esults fom tis assumtion ill still be actically useful, esecially fo comanies ic intend to develo elevant univese equiments fo tis non-exlosive tecnology. Futemoe, e do not take into account te ossible lastic defomation of te ock in te esent eseac, neite te ceation no te oagation of cacks, ic ill be ou futue study. Consequently, e ave tee aametes to descibe te ock: Young s modulus E, Poisson's atio! and it's density!. 6
2.3 Contact simulation As son in Fig. 1 and Fig. 2(a), tee ae tee ais of contacts involved in te imact ocess, i.e., te contact beteen te iston and te ate, te contact beteen te iston and te ock, and te contact beteen te ate and te ock. We use te ad contact algoitm fom ABAQUS itout daming to simulate tese contacts. Te fiction is also neglected in ou simulation. Pactically, te fiction beteen ate and iston o ock sould be vey lo. Fute study ill be caied out afte e obtain eliable fiction value involved in te contact beteen iston and ock. All te imact simulations ee caied out by using ABAQUS/Exlicit. Te effect of te ydaulic imact is evaluated by te lagest incile stess in te ock. As an examle of ou finite element simulation esults, Fig. 3 sos te distibution of te maximum incial stess field in te stuctue at te instant en te sockave aives at te end of te bottom of te ole. It clealy indicates tat te lagest maximum incial stess, te lagest incial stess in sot, occus at te bottom of te ole. Iesective of micostuctues, cacks ill ossibly initiate at tis osition it tis lagest stess in te ock. Fig. 4 sos te coesonding diection field of te maximum incial stess at tis local aea in te ock. On te suface, te diection of te maximum incial stess is eendicula to te suface. One can imagine, once cacks initiate, te igly essuized ate ill enetate into te cacks and dive te cacks to oagate, ic ill be te coe of te investigation to undestand te ock beaking in ou futue study. 3. Dimensional analysis 7
All te aametes involved in te simulation ae listed in Table 1. Hee, te adius of te iston is te same as te adius of te boeole. Dimensional analysis is a oeful metod to systematically cay out aametical study on a comlicated oblem involving many aametes, see examles [8-10]. Tis metod is alied in te cuent investigation. Te objective vaiable in ou dimensional analysis is cosen as te lagest incial stess in te ock,! m, duing an imact ocess. Te ock mateial can be ougly consideed as bittle mateial. Accoding to Coulomb s citeion of maximum nomal stess, te lagest incial stess ill initiate cacks in te ock and lead to te fagmentation of ock mass. Geneally, te lagest incial stess is a function of all te aametes listed in Table 1, i.e., m ( L,E,,,V,D,E,,,R,D,R a,e,, )! = f " # " # " #. (1) Accoding to te Buckingam! -teoem fo dimensional analysis, e can educe te numbe of aametes. Fo tis uose, e coose D, te det of te ole,!, te density of te iston and E, te Young modulus of te iston as te imay quantities. Teefoe, te dimensionless function fo te lagest incial stess is * " L V m D E + R R a E + # = $ 1,,,,,,, 1/ 2 1/ 2,,,,,,,!. (2) E % D E ' D E D D E & ( + + + ) Among all te dimensionless aametes tat e ave just ceated, some values can be consideed as uncanged in tis ysical oblem. Te iston is geneally made fom steel and ate is nomally used as te liquid in tis tecnology. Teefoe, te mateial data fo te iston and te ate can be teated as constant. Consequently, te folloing dimensionless aametes ill be consideed constant in ou model:! = 0.3,! = 0.4995, (3) 8
E 6207813 31 10 11 E = 2! 10 =! 6,! 1000 0.128! = 7800 =. (4) Teefoe, te dimensionless function (2) can be simlified as * " L V m D R R a E + # = $ 2,,,,,,, 1/ 2 1/ 2,!. (5) E % D E ' D D D E & ( + + ) Afte tis dimensional analysis, te numbe of vaiables involved in te stess analysis as educed fom 15 in te oiginal Eq. (1) to 8 in Eq. (5). We no define te domains of te dimensionless vaiables based on ou undestanding of tis ysical oblem. Te folloing limits of te domains fo geometical aametes ae aoiated fo tis oblem: L [ 0.1;0.8 ] D!, [ 0.1;0.8] R [ 0.01;0.5 ] D!, a [ 0.001;0.05] D D!. (6) R D!. (7) Refeing to [11], te domains of te mecanical oeties of diffeent tyes of ocks ae son in Table 2. Accoding to tis table, afte coosing E = 200 GPa and 3! = 7800 Kg / m, e can define te domains fo dimensionless vaiables linked to te ock mateial as follos: E [ 0.05;0.5 ] E!, [ 0.1;0.35]! ", [ 0.25;0.4]!! ". (8) Accoding to Denisat et al. [5], te initial velocity of te iston can vay fom 10 m / s to 200 m / s, ic coesonds to te folloing domain of te dimensionless initial velocity: V # E! " 1/ 2 1/ 2 $ [ 0.0020;0.0395]. (9) 9
In ou numeical simulations, e ave to adjust te limits of some aametes domains because of numeical instability oblem. Te Poisson s atio of ate is 0.4995, ic is close to te value of 0.5 of imcomessible mateials. Additionally, te ate is igly confined in te boeole and exosed to a igly comessive load fom te imact of te ig seed iston. Due to tese factos, te stiffness matix in a finite element simulation is almost singula, ic can sometimes lead to numeical instability [12]. A unsuccessful numeical instability calulcation can be easily detected by obseving lage abnomally distoted and enetated defom meses. To ovecome tis instablility oblem, e sometimes ave to coose some values loe tan te ue limit o ige tan te loe limit of te domains defined in above Eqs (6-9). In te folloing section, only te coect esults fom te stable calculations ae eoted. We can believe tat te fitted las in te esticted domains of study in te folloing section ae valid in te entie domains defined in Eqs (6-9). 4. Results and discussions 4.1. Influence of ock oeties Te effect of ock density is consideed fist. Fig. 5 sos te influence of te nomalized ock density,! /!, on te nomalized lagest incial stess,! / E, in te ock duing te imact ocess. We ave consideed te to limit values of te domains of all te dimensionless aametes in Eq. (5), one by one fom Fig. 5(a) to Fig. 5(g), ile fixing te values of all te otes dimensionless aametes at te middle values of tei domains, ic ae defined in Eqs. (6-9). Fo examle, te to cuves in Fig. 5(a) ae obtained fo L / D = 0.17 and L / D = 0.58 esectively ile fixing v = 0.19, E / E = 0.3, m P R / D = 0.026, R / D = 0.26, D / D = 0.5 and a V! 1/ 2 1/ 2 /( E ) = 0.013 ". 10
Figs. 5(a-g) clealy indicate tat te vaiation of te nomalized lagest incial stess! / E due to te cange of te nomalized ock density! /! fom 0.25 to 0.4 in all te m studied cases is negligibly small. Because all te studied cases ave coveed te domains of tis ysical oblem, one can deduce tat it is geneally coect tat te influence of te vaiation of ock density on te maximum lagest incial stess in te ock can be neglected. Consequently, te dimensionless ock density in Eq. (5) can be emoved and te dimensionless stess function can be fute simlified as * " L V D R R a E # m = $ 3,,,,,, + 1/ 2! 1/ 2. (10) E % D E ' D D D E & (, ) Fig. 6 sos te numeical esults of te nomalized lagest incial stess in te ock duing te imact fo diffeent values of te Poisson's atio of te ock. Similaly, all te otes dimensionless aametes in Eq. (10) ae fixed at tei middle values of tei domains, and only te Poisson's atio of te ock canges fom one calculation to anote. We can see tat te nomalized lagest incial stess inceases sligtly it te inceasing of te Poisson s atio of te ock. Fo examle, if E = 200 GPa, 3! = 7800 Kg / m, D 60 = cm, L = 20 cm, V = 60 m / s, D = 30 cm, R = 5 cm, R = 5 mm and E = 50 GPa, a accoding to Fig. 6, ten te lagest incial stess in te ock inceases fom 862 MPa to 954 MPa en te Poisson's atio of te ock evolves fom 0.1 to 0.35. As son in Fig. 6, te set of te numeical data can be ell fitted by te folloing exonential function: " m 2.98 0.0043 0.0107 E = +! #. (11) Fig. 7 sos te vaiation of te nomalized lagest incial stess in te ock duing te imact fo diffeent nomalized values of te Young's modulus of te ock. Simila to Fig. 6, 11
! / E inceases sligtly it te inceasing of E / E fom 0.1 to 0.5. Fo examle, if m E = 200 GPa, 3! = 7800 Kg / m, D 60 = cm, L = 20 cm, V = 60 m / s, D = 30 cm, R = 5 cm, R = 5 mm and! = 0.2, e see fom Fig. 7 tat te lagest incial stess in te a ock evolves fom 746 MPa to 934 MPa en te Young s modulus of te ock evolves fom 10 GPa to 100 GPa. Te set of te numeical data is also fitted by an exonential function, ic is son it te tick cuve in Fig. 7. 4.2. Influence of boeole dimensions 4.2.1 Boeole det Te det of te boeole, D, is cosen as te imay lengt in te dimensional analysis. Its influence on te oblem can be imlicitly eflected in te aametic study of ote dimensionless lengt aametes, suc as te dimensionless iston lengt and te dimensionless ate det. But it is undestandable tat te det of te boeole as no diect influence on te lagest incial stess in te ock, and tat is te eason to coose it as te imay lengt to nomalize te ote aametes. 4.2.2 Boeole adius Fig. 8 sos te influence of te nomalized boeole adius R / D on te nomalized lagest incial stess in te ock! / E ile ote aametes ae fixed at te middle m values of tei domains. It indicates tat! / E inceases gadually it R / D. Bea in m mind, te boeole adius is equal to te adius of te ate column and te adius of te iston. Inceasing boeole adius means inceasing te adius of te iston, and teefoe, inceasing te initial kinetic enegy of te iston it fixed initial velocity. Tis influence in eal value is vey significant. Fo examle, if E = 200 GPa, 3! = 7800 Kg / m, 12
D = 60 cm, L = 20 cm, V = 60 m / s, D = 30 cm, E = 50 GPa, R = 5 mm and a! = 0.2, ten te lagest incial stess in te ock evolves fom 842 MPa to 2244 MPa en te boeole adius evolves fom 5 cm to 30 cm accoding to te numeical esults. It is inteesting to lot te instantaneous aveage velocity and te instantaneous kinetic enegy of te iston ove te imacting time fo seveal values of te dimensionless adius of te ole. Fig. 9 and Fig. 10 so tese esults. In Fig. 9, e can see tat at te beginning, te iston is moving don, tat is y te aveage velocity is negative. Ten its aveage velocity deceases, and at t 1/ 2 1/ 2 7 D! E " =, te iston as zeo aveaged velocity. Afte tat, te # # iston is coming u, so its aveage velocity is inceasing. We can also follo tis in Fig. 10: te iston stats it its kinetic enegy, ic deceases until t 1/ 2 1/ 2 7 D! E " = # # ee it is null, and ten inceases because te iston is coming u. Additionally, e can see fom Fig. 9 tat te aveage velocity of te iston does not deend on te boeole adius, and fom Fig. 10 tat te kinetic enegy of te iston deends on te adius of te ole, ic is obvious because te adius of te ole is also te adius of te iston and te initial kinetic enegy stongly deends on te adius of te iston. Hoeve, e can see tat its evolution is quite simila fom one value to anote, ic is obviously linked to te fact tat te aveage velocity is te same fo all cuves in Fig. 9. We can exlain tis by saying tat bot te kinetic enegy of te iston and te enegy tat is tansmitted to te ate deend on te adius of te iston in te same ay: tey bot ae ootional to te coss section aea of te iston, i.e., te squae of its adius. Ten, if te iston as a lage adius, it ill ave moe initial kinetic enegy, but it ill also tansmit moe enegy to te ate, so its kinetic enegy ill decease faste. Tis emak is imotant, and e ill exlain belo tat te kinetic enegy of te iston is a key facto to detemine te lagest incial stess in te ock. 13
To undestand tis, e discuss an imact ocess by folloing Fig. 11, ic sos te fist incial stess in te element tat as te lagest incial stess and te instantaneous aveage velocity of te iston vesus imacting time fo R D = 0.0167 : - Te iston its te ate it its initial velocity at te beginning of te simulation, ic stats te imact ocess. - Te ceated sockave comes don in te ate, and aives at te bottom of te boeole at t 1/ 2 1/ 2 2 D! E " =. Hee is te fist eak in te stess cuve, it # #! 3 # E = 1" 10. - Ten te sockave climb back to te suface (te mateial beaviou of te ate is vey diffeent fom te otes mateial beavious, so te tansmission of enegy is lo) and te stess at te bottom of te ole educes because of te disesion of enegy. - Wen te sockave aives at te suface at t 1/ 2 1/ 2 4 D! E " =, it is eflected # # and comes don again, but it moe enegy because te iston is still coming don. - Tus, te second eak in te stess cuve ill be geate, it! 3 # E = 1.7 " 10 at t D 1/ 2 1/ 2 6! E " = # #. - And en te sockave climb back and aives at te suface fo te second time, at t 1/ 2 1/ 2 8 D! E " =, te iston as no moe velocity donad and is going u. # # - So te sockave comes don again it less enegy, and te tid eak in te! 3 stess cuve ill be smalle, it # E = 1.6" 10 at t 1/ 2 1/ 2 10 D! E " =. # # 14
We can conclude tat e ave te lagest incial stess in te ock en te sockave aives at te bottom of te ole te last time ile te iston still aving some velocity donad. It indicates tat te kinetic enegy of te iston lays an imotant ole in te detemination of te lagest incial stess. 4.2.3 Ac adius at boeole bottom Tis aamete, te ac adius at te boeole bottom, as son in Fig. 2, is intoduced to avoid te oblem of infinite stess at te cone and allo a bette modelling of te geomety of te ole in a eal situation. Obviously, it ill ave a substantial influence on te lagest incial stess in te ock. Fig. 12 sos its influence on te oblem. Te tick cuve in Fig. 12 eesents an exonential function to fit te numeical dots. We can see tat te stess tends to infinity en te adius of te ac closes to zeo, ic is nomal because of te oblem of singulaity en R = 0 mm. Pactically, tis aamete ill neve be equal to a zeo, and its value can be estimated fom te documentation of te active at of te tool used to dill te ole, in addition to te consideation of te ock mateial, o fom exeimental tests. We can acieve te dimensional values fom Fig. 12. Fo instance, if E = 200 GPa, 3! = 7800 Kg / m and D 60 = cm, L = 20 cm, V = 60 m / s, D = 30 cm, E = 50 GPa, R = 5 cm and! = 0.2, te lagest incial stess in te ock educes fom 1860 MPa to 538 MPa en te adius of te ac at te bottom of te ole inceases fom 1 mm to 10 mm. 4.2.4. Wate det Fig. 13 sos te influence of D on te lagest incial stess in te ock and on te time to eac tis value, en all te ote dimensionless aametes ae fixed at te middle values of 15
tei domains. We can see tat te lagest incial stess deceases and tat te time to eac tat stess inceases en te det of ate inceases. Tis conclusion can be exlained by te fact tat te deee te ate is, te moe te enegy can disese fom te ate to te ock, and teefoe, it esults to a smalle lagest incial stess in te ock at te bottom of te ole. Tis elationsi deends on te distance tavelled by te sockave, and Fig. 13 indicates tat te nomalized stess cuve consists of to linea ats it te cone at D D = 0.35. Futemoe, te sloe of te nomalized stess cuve deends on te numbe of etun tis tat te sockave as made befoe te lagest incial stess is eaced and te cange of te cuve s sloe is linked to te discontinuity of te cuve fo te time to eac te lagest stess, and is exlained in detail belo. Te vaiation of te time to eac te maximum incial stess it te cange of te ate det, son in Fig. 13, is due to te combination of to facts: - en te det of ate inceases, te time fo te sockave to tavel fom te suface of te ate to te bottom of te ole inceases too, so te time to eac te lagest incial stess inceases. - and en te ate becomes dee enoug, te lagest incial stess is not eaced at te tid time en te sockave aives at te bottom of te ole, but te second time. We can follo tis in Figs. 14(a) and 14(b), ic give te fist incial stess in te element tat as te lagest incial stess in te ock and te kinetic enegy of te iston vesus times, esectively fo D D = 0.333 and D D = 0.417, ic ae esectively aound te cone of te stess cuve and te doing at of te time cuve in Fig. 13. Fig. 14(a) sos tat te lagest incial stess is eaced at te tid time en te sockave aives at te bottom of te ole fo D D = 0.333 and Fig. 14(b) sos it is eaced at te second 16
time fo D D = 0.417. Tis is te eason fo te time doing beteen D D = 0.333 and D D = 0.417 and te aeaance of te cone of te stess cuve in Fig. 13. Fig. 13 indicates tat educing te ate det can incease te lagest stess in te ock. Fo examle, in te case of E = 200 GPa, 3! = 7800 Kg / m, D 60 = cm, L = 20 cm, V = 60 m / s, R = 5 mm, E = 50 GPa, R = 5 cm,! = 0.2, te lagest incial stess in a te ock inceases fom 773 MPa to 1207 MPa en te det of ate in te ole educes fom 50 cm to 10 cm. In tems of te entie ock beaking tecnology, e need essuized ate to dive cack oagation once cacks ae initiated in te ock. Teefoe, it is not ecommended to incease te lagest incial stess in te ock, te cack initiation focing, by educing te ate det. 4.3. Influence of iston dimensions 4.3.1. Piston lengt Te adius of te iston is te same as R, te adius of te ole. Its influence as been studied in te evious subsection. No, let s conside te influence of iston lengt. Fig. 15 sos tat te nomalized lagest incial stess inceases continuously it te inceasing of te nomalized iston lengt. Te longe te iston is, te ige its initial enegy is because of te fixed initial velocity. Teefoe, te stess in te ock inceases. Suc an influence is significant. Fo examle, in te case of E = 200 GPa, 3! = 7800 Kg / m, D = 60 cm, D = 30 cm, V = 60 m / s, R = 5 mm, E = 50 GPa, R = 5 cm and! = 0.2, a e obtain fom Fig. 15 tat te lagest incial stess in te ock evolves fom 690 MPa to 1202 MPa if te iston lengt evolves fom 10 cm to 50 cm. 17
Fig. 15 also sos tat te time to eac te lagest stess as an iegula elationsi it te iston lengt. Tis can be exlained by Figs. 16(a-c), ic so te elationsis beteen te nomalized fist incial stess in te element tat as te lagest value in te ock duing te imact, te nomalized kinetic enegy of te iston and te nomalized imacting time fo diffeent values of te nomalized iston lengt, L D = 0.1667 in Fig. 16(a), L D = 0.4167 in Fig. 16(b), and L D = 0.5833 in Fig. 16(c), ile fixing te ote dimensionless aametes at te middle values of tei domains. Fig. 16(a) indicates tat en te sockave climbs back to te suface at te second time en te sloe of te cuve of te kinetic enegy canges, at t 1/ 2 1/ 2 7.5 D! E " =, te iston as no moe # # velocity donad and is coming u (its kinetic enegy as aleady been null), ic means tat all its enegy as aleady been tansfeed to te stuctue, so te lagest incial stess as aleady been eaced, te second time en te sockave aives at te bottom of te! 3 ole (# m E = 3.5" 10 at t 1/ 2 1/ 2 6 D! E " = ). It is exactly te same ocess as in # # evious Subsection 4.2.2. In te Fig. 16(b), te imacting ocess is simila: te lagest incial stess is also eaced at te second time en te sockave aives at te bottom of te ole, at t 1/ 2 1/ 2 6 D! E " =, but due to te ige imacting enegy, te value of te # # nomalized lagest stess is lage, it! m E " 3 = 4.5# 10. And Fig. 16(c) is fo an even longe iston: e see ee tat te iston still ave some donad velocity (its kinetic enegy as not been null) en te sockave etuns at te suface fo te second time at t D 1/ 2 1/ 2 7.5! E " = # #. Teefoe, te lagest incial stess is eaced at te tid time en te sockave aives at te bottom of te ole:! m E " 3 = 5.3# 10 at 18
t D 1/ 2 1/ 2 10! E " = # #. Tis is te eason y te time to eac te lagest incial stess is iegula as son in Fig. 15. 4.3.2. Piston s initial velocity Fig. 17 sos te vaiation of te nomalized incial stess in te ock it te cange of te nomalized initial velocity of te iston. It clealy indicates tat te nomalized stess inceases linealy it te nomalized velocity and te vaiation ate is significant. Fo examle, in te case of E = 200 GPa, 3! = 7800 Kg / m, D 60 = cm, D = 30 cm, L = 20 cm, R = 5 mm, E = 50 GPa, R = 5 cm, and! = 0.2, te lagest incial stess a in te ock evolves fom 700 MPa to 2800 MPa en te initial velocity of te iston evolves fom 50 m / s to 200 m / s. 4.3.3. Initial kinetic enegy of te iston We ave investigated te influence of te dimensions of te iston and its initial velocity on te lagest incial stess in te ock. We ill no ty to undestand te global influence of its initial kinetic enegy, ic embace all tese aametes: 1 2 2 K = #! #" # R # L # V. (12) 2 Fig. 18 sos te evolution of te nomalized lagest incial stess in te ock duing te imact it esect to te nomalized initial kinetic enegy of te iston. Te initial kinetic enegy is canged by tee aoaces seaately, i.e., canging te iston lengt, canging te iston adius and canging te initial velocity of te iston, ile keeing te ote aametes fixed at te middle values of tei domains. Numeical esults fom te tee aoaces ae deicted by tee cuves in Fig. 18. All tese cuves indicate tat inceasing te initial kinetic enegy can incease te lagest incial stess in te ock, ic is not a 19
suise. Fo te uose of inceasing te lagest stess in te ock ove 800 MPa fo E = 200 GPa toug inceasing te initial kinetic enegy, Fig. 18 indicates tat te most effective ay is to incease te iston s initial velocity. 5. Conclusions Te ydaulic imact oblem of a non-exlosive ock beaking tecnology as been studied. Dimensional analysis and te finite element metod ave been alied to systematically investigate te influence of all te aametes involved in te imact ocess, ic includes te geometical aametes and te oeties of ock, iston and ate. Majo conclusions fom ou investigation ae summaized belo: - Te ock density as a negligible influence on te lagest incial stess in te ock. - Te influences of ock s Poisson's atio and Young's modulus on te lagest incial stess in te ock ae small. - Te sae of te bottom of te ole as a substantial imact on te oblem. Fo examle, te close it is to a igt angle, te lage ill be te lagest stess in te ock. - Te lagest incial stess in te ock deceases if te det of ate is inceased. - Inceasing te initial kinetic enegy of te iston as a significant influence on te oblem: it imlies an incease of te lagest incial stess in te ock and a vaiation of te time to eac tat value. - Te best ay to incease te lagest incial stess in te ock by inceasing te initial kinetic enegy of te iston is to incease its initial velocity. Acknoledgement 20
Tis ok as been atially suoted by te Austalia Reseac Council. Many tanks to Lauent Camaney fo is useful Pel scits. Refeences 1. Sing, S. P.: Non-exlosive alications of te PCF concet fo undegound excavation. Tunnelling and Undegound Sace Tecnology 13 (1998) 305-311 2. Young, C.: Contolled foam injection fo ad ock excavation. In 37 t U. S. Rock Mecanics Symosium (1999), Vail, Coloado 3. McCaty, D. E.: Metod aaatus and catidge fo non-exlosive ock fagmentation. U. S. Patent (1998) No. 5803551 4. Young, C.: Contolled foam injection metod and means fo fagmentation of ad comact ock and concete. U. S. Patent (2002) No. 6375271 5. Denisat, J. P.; Edney, B. E.; Lemcke, B.: Metod of beaking a ad comact mateial, means fo caying out te metod and alication of te metod. U. S. Patent (1976) No. 3988037 6. Wilson, E. L.: Tee-dimensional static and dynamic analysis of stuctues. 3 d Edition. Bekeley: Comutes and Stuctues, Inc. 2002 7. Jaege, J. C.; Cook, N. G. W.: Fundamentals of ock mecanics. 3 d Edition. London: Caman and Hall, 1979 8. Andeson, T. L.: Factue mecanics: Fundamentals and alications. 2nd Edition, Boca Raton: CRC Pess, 1995 9. Tunvisut, K.; O Dod, N. P.; Busso, E. P.: Use of scaling functions to detemine mecanical oeties of tin coatings fom micoindenation tests. Intenational Jounal of Solids and Stuctues 38 (2001) 335-351 21
10. Yan, W.; Sun, Q.; Feng, X.-Q.; Qian, L.: Analysis of Seical Indentation of Sueelastic Sae Memoy Alloys. Submitted to Intenational Jounal of Solids and Stuctues. 11. Russell Mineal Equiment Pty. Ltd. Reot. 2003. 12. ABAQUS v. 6.4 Analysis/Teoy Manuals. 2003. 22
Table 1. List of all te aametes involved in te imact simulation. Piston Wate Rock Boeole E : Young s modulus E : Young s modulus E : Young s modulus R : adius! : Poisson's atio! : Poisson's atio! : Poisson's atio D : det! : density! : density! : density R a : ac adius L : lengt D : det V : initial velocity 23
Table 2. Mecanical oeties of tyical ock mateials. Rock mateial Density (Kg / m 3 ) Young modulus (GPa) Poisson s atio Ganite 2500-2800 35-80 0.1-0.2 Basalt 2400-2900 20-100 0.1-0.3 Sandstone 2200-2700 10-40 0.2-0.3 Doleite 2900-3100 40-90 0.1-0.3 Limestone 2000-2800 10-50 0.2-0.35 Andesine 2500-2800 30-60 0.1-0.25 24
ig seed iston ock boeole ate cacks Fig. 1. Illustation of te ydaulic ock beaking tecnology. 25
Piston Wate Rock Axisymmetic axis Fig. 2(a) 26
Fig. 2(b) Fig. 2. Finite element mes and elevant geometical aametes: (a) global mes; (b) local mes aound te bottom of te boeole. 27
Fig. 3. Maximum incial stess field, in te stuctue. 28
Fig. 4. Diection field of te maximum incial stess, in te ock at te bottom of te ole. 29
Fig. 5(a) Fig. 5(b) 30
Fig. 5(c) Fig. 5(d) 31
Fig. 5(e) Fig. 5(f) 32
Fig. 5(g) Fig. 5. Influence of nomalized ock density on te nomalized lagest incial stess in te ock fo te cases (a) L / D = 0.17 and L / D = 0.58 ; (b) v = 0.01 and v = 0.35 ; (c) E / E = 0.1 and E / E = 0.5 ; (d) R / D = 0.0017 and R / D = 0.05 ; (e) R / D = 0.017 P a a and R / D = 0.5 ; (f) D / D = 0.17 and D / D = 0.83 ; (g) V! 1/ 2 1/ 2 /( E ) = 0.002 " and V! 1/ 2 1/ 2 /( E ) = 0.024 ". 33
Fig. 6. Influence of Poisson's atio of te ock on te nomalized lagest incial stess in te ock duing te imact. 34
Fig. 7. Influence of nomalized Young s modulus of te ock on te nomalized lagest incial stess in te ock duing te imact. 35
Fig. 8. Influence of nomalized boeole adius on te nomalized lagest incial stess in te ock duing te imact. 36
Fig. 9. Nomalized aveage velocity of te iston vesus nomalized imacting time fo seveal values of nomalized boeole adius. 37
Fig. 10. Nomalized kinetic enegy of te iston vesus nomalized imacting time fo seveal values of nomalized boeole adius. 38
Fig. 11. Nomalized enegy of te iston and te nomalized maximum incial stess in te element tat as te lagest incial stess in te ock duing te imact vesus nomalized imacting time, fo R D = 0.0167. 39
Fig. 12. Influence of nomalized ac adius at te bottom of te ole on te nomalized lagest incial stess in te ock duing te imact. 40
Fig. 13. Influence of nomalized ate det on te nomalized lagest incial stess in te ock duing te imact and nomalized imacting time to eac tat stess. 41
Fig. 14(a) Fig. 14(b) Fig. 14. Nomalized kinetic enegy of te iston and te nomalized maximum incial stess in te element tat as te lagest incial stess in te ock duing te imact vesus nomalized time fo (a) D D = 0.333 and (b) D D = 0.417. 42
Fig. 15. Influence of nomalized iston lengt on te nomalized lagest incial stess in te ock and te nomalized time to eac tat stess. 43
Fig. 16(a) Fig. 16(b) 44
Fig. 16(c) Fig. 16. Nomalized kinetic enegy of te iston and nomalized fist incial stess in te element tat as te lagest incial stess in te ock duing te imact vesus nomalized imacting time fo (a) L D = 0.1667, (b) L D = 0.4167 and (c) L D = 0.5833. 45
Fig. 17. Influence of nomalized initial velocity of te iston on te nomalized lagest incial stess in te ock duing te imact. 46
Fig. 18. Influence of nomalized initial kinetic enegy of te iston on nomalized lagest incial stess in te ock duing te imact alying diffeent ays to incease te initial kinetic enegy of te iston. 47