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Determination of the Inelastic Parameters of Geologic Materials from Incremental Creep Experiments

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Determination of the Inelastic Parameters of Geologic Materials from Incremental Creep Experiments e +wy.&J,A , e .-. SOCIETY OF PETROLEUM ENGINEERS OF AIME 6200 North Central Expressway ~m#R $3F’E 170’7 Dallas, Texas i’5206 THIS IS A PREPR2VT --- SUBJECT TO CORRECTION Determination of “the Inelastic Parameters Downloaded from http://onepetro.org/SPEDRM/proceedings-pdf/67DRM/All-67DRM/SPE-1707-MS/2087759/spe-1707-ms.pdf by guest on 02 October 2021 -. .-.,.,.....:. .+._. .. .. .. ufGeologi c.Materi-als .Trcm .. .. By H. Reginald Hardy, Jr., Fennsylv~nic S%te University, University Park, pa” t) Col)YriKht 1967 Amrrirrm Instilute of 11inin~, }Waiiurgid and Prlrolrum Enginrcrs, Inc. ——. IIWH701XJCTION br:adly outlined as follow~: In spite of the increased research cm the “To study experimentally the mechanical behavior of geologic materials which has been r-whaviorof selected geologic materials and undertaken in recent years, many of the mast analyze these experimental data using the important mechanical properties have nr.)tbeen concept 01 mechanical model~ and the analyti investigated in detail. In particular the mcthotisof viscoclzsticity. In particular t effect of time has received very little attcn- tievelopgovefning equativns far these materi tion from the experimental point of view, cxisedoc suitable laboratory experiments and although its im]mrtance has been suggestsd b; valid at least within a range of stre~s, con many worker%. Many wvrkers have reported that fi,ning])ressure,duration of loading, anti “test “resultsappetiredto be influenced by the temperature consistent with’pr.mcticalo,ppli rate and duraticn of loading, although few have tions..” .. beenwilling to accept the fact jhat such ‘ ;;- .. .. .. ... .~... ... ... .. ..... bchavi.oris indicative of an inelastic.material. ~“e .first.phasetifthis.$esearch ~f~grt Lncluded the experimental investigation uf t . .4general study of the mechanical proper- inelastic behavior of.a number of “simple’”. ties of geologic materials”was initiated in @910gic materials using incremental creep 1951 in The Mining Research Section of the experiments, and the associated development Fuels and Mining Practice Division, Mines the necessary experimental facilities and Branch, Canadian Dept. of Energy, Mines and analytical methods. This paper outlines bri Resources, as part of a ftmdaanentalstudy of the experimental and analytical technique bround stress in Canadian Coal Mines.1 The developed, and presents experimental result initial work was restricted to short-period for the initial deformation studies carried tests on typical mine rock under uniaxial on Wombeyan marble. compressive stress, but as the importance of the “time factor” became more abvious, studies THEORY were undertaken to investigate time-dependent behavior; These.ktuditis,which were initiated Papers de”alingwith the behavior of in 195’(,consisted mainly of a comprehensive geologic materials are found to be widely literature search on the subject, and the dispersed throughout the literature. Howeve initial.development of experimental facili- extensive bibliographies dealing with the ties.2?3 This research project was inactive general mechanical properties of these mater during the period 1959-1961 due in part to the als have beck $ublished recently by Griggs - -relocation. .=— of-labo”ratory. facilities;’- :. -- Hahdin4 and”MitraandWillson.5- In”the more specific field-of time:depe~dent behavior of ~ the fall of.1961 the.project”wbs.reacti-. .geologic.material.s..extensive.bibliora hies vated l~iththe propos_edresearch program being have been.~iven in papers Y Hardy> ! ..—.-. - . -.— -@d ~sra;”{”,~d”Robefisoni=.8.. ~ .8~urre ..*pre~e-ntl,yat ,Thepennsy-l”v&iaS.tai.e-UO) ... :.:.-.:--” .. .Un~versity P&$k~;,Pa;‘“ “ ‘. ., . :“ . ‘“ ““ .TheVmqJority~of ekpe~iqents’con~ucted. Re?erencei”an”d’illus%?ations-”atend of pape”r..- - investigate the time-dependent behavior of experiment] is found to be geologic materials have been creep experiments carried out under conditions of constant applied load. [The term “creep” wi.llbe defined, in a general sense, throughout this paper 0.6the time-dependent strain observed in a material under a condition of constant str~ss:] Numerous empirical equations have been 6eveloped to describe this time-dependent Downloaded from http://onepetro.org/SPEDRM/proceedings-pdf/67DRM/All-67DRM/SPE-1707-MS/2087759/spe-1707-ms.pdf by guest on 02 October 2021 behavior;“however,it is the author’s opinion that the phenomenological approach providefia: more convenient representation; Here the behavi~r-vft.he material is expressed.in terms of a combination of a numbe”r“ofsimple where e[t] is the time-dependent strain, Un is mechanical models. According to Freudenthal, the mabaitude of the constant stress, t is the “the theory of mechanical models considers time, T is the retardation time defined as combinations of elements which are supposed to behc.vemechanically like the constituent phases of the material but which, apart from the material behavior, have nothing in common with the real material.”9 A number of mechanical 7-=4/’=, . ..[31 models heve been postulated to explain the inelastic deformation of various geologic materials. and El, E2) Nl, and N2 are the mtidelParQ$neter$ The use of mechanical models to describe To investigate the creep behavior of the the deformation behavior of geologic materials test material at various compressive stress haG been discuss~~ by a number of writers in- ievels it was f.mnd convenient co u~e incre- cluding Hard 2~o~10)ll Price,12 Ijnan,13Ito mental loading. ~ this case the specimen and Terada,l{’H~t$15 Attvell,16,1”(s~lu~to. stress was increased in a number of small wicz,18 Tida and Kumazawa,19 Terry,20 increments A:&. After each increme& t the lfiatsushima~land Litwiniszym.22 A review of resulting stresson was maintained co%stant at the Ceneral application of Viscoelasticity, the level for a period of tinw t~, such that including the mechanical model concept, to the tn>> T in which case the factor exP [-t/l’]+Ot behavior of geologic material Under these conditions the strain el[t] deveL- lished recently by Robertson:B ‘a’ been ‘ub- oped during the incremental loading and the peri;d”tn .o? cqnst~t. stress $ollu.wwing,it w~ll ... 21.. ““10 ll”[~t,sushtiaj ‘beofthe form - Studies by Hardy, ~ .. .. ... Pri;e12”aid”othei% Orirock, by.Tek?ry20tincoal and by ROSS23 on.,concrete[a material.in many ways similar to-geologic materials] indicate that deformation of these materials under sus- tained loading may be analyzed satisfactorily in terms of the Burgers model, illustrated in Fig. 1. The theoretical behavior of this model has been investi ated in detail by Frederick and Garcia,2f and more recently by Steppel.25 The governing equation is found to [1,] be . ...0. ● . Al where all factors have been defined previously ~2: F+ /+5’+4! &- (’)[ ‘4”- #ya This may be written as 1 .. ~ere k.~d-e’”are, re~pe-ctivelyjth-est~ess-aud. “.w~ere “&~ ~s””thkinitan”t~kous elastic”~t”rati’ strain, and El, E2, Nl, and,N2 are the=m~del produced by.the stress increment A~n, ~d en[~] -.-... par&meters.’- ‘“ -“’”- . ‘ is-the time-dependent [creep]-”strain”which-”’. ..- . occurs+at,.$he.const~t-”stres”s<n~.. Therefore ‘The solut~og”’=ofthego~erniqg equati?n-for ““,,.-. <”;.”:... ;-: .:.’.. the :ond%tlon o’f:c?nstsxrtstress:[creep . - .. .. .. --- , . ... .. ., ,. .- , -. ,.. , , 1 Puel-7c)7 H. RFX2TNAT,T) HAHT)Y. ,TR. stress compatible with the writer’s experi- mental facilities, A supply of this material in the form of ‘(/8-in.diameter core was kindly made available by M. S. Paterson of Th ‘m’’)=.~[’”+~”~1Australian NatiorialU., Canberra, Au6tralia. I Apparatus and Experimental Technique .+ +29 . ..[61 Deformation expertients were conducted Downloaded from http://onepetro.org/SPEDRM/proceedings-pdf/67DRM/All-67DRM/SPE-1707-MS/2087759/spe-1707-ms.pdf by guest on 02 October 2021 in a test enclosure which was designed to pro .. ,-..... > .,.:.....b A? ,..,.,,..-. .. ..:,... .,,. .. .. .’:: ‘- ...- , vide controlled temperature conditionsof 70 ? and l/10F. Cylindrical test specimens, nominally 3/1+in. in diameter and l-3/~ in. in length were machined from diamond drill core ushig ‘ lathe and an attached tool post grinder [see’ Aez = Aq/Ea. [71 Ref. 28.] To measure axial strain a set of three foil-type resistance strain gauges were mounted at 120° intervals around the circwn- EXPER~4ENT ferencc of the tect speeb~en. Fig. 2 shows a set of strain-gauged spec~mens ready for Introduction testing. Relatively few workers have undertaken the T& Gpecirqens‘,leremounted in a loading investi~ation of the inelastic “behaviu~of jig and compressed axially using a specially geologic materials. This has been due in part designed loading system. Complete details of to the many experimental difficulties that must this system have been described in recent ?6 11,29 ~i~ sys.;em, which is be overcome if significant data are to be publications.- > obtained. As a result considerable time has illustrated in Fig. 3, is basically an “on-of been spent by the author in developing a pneumatic-hydraulic servo-luadin~ system whic suitable e~erimcntal facility fur such inves- may be vperated in a variety of test modes. tigations. A description of the design and the incremental ~trcss mode the specimen stre eonstruc~ion oi”this facility has been p’iJ- may be increased in a number of rapidly appli lished,2b Therefore, this aspect of zhe small increments. After each increment the program will be discussed only briefly in this stress may be maintained constant for n peyio paper. of time during which the resulting creep stra is observed ahd recorded. At the end of this ,. ..Test-Material ~ -- - . - perio$,.thestress Tai be-ihcie?sed.;o the nex level. Using this system it.hasbeen possibl Until recently, engineers and in partic- ttiapply incr~mental’-stressesof up to 1,000 ular mining engineers have been concerned psi in period? of less than four ~econds and. mainly with the beh~vior and properties of the maintain the stress constant to within ? 1/10 specific local geologic materials with which per cent at each level.
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