Determination of the cutting resistance model of soil. Jozef Karol Szymanski* and Saleh Balideh

Size: px

Start display at page:

Download "Determination of the cutting resistance model of soil. Jozef Karol Szymanski* and Saleh Balideh"

Elaine Edwards
6 years ago
Views:

1 220 Int. J. Mining and Minral Enginring, Vol. Dtrmination of th cutting rsistanc modl of soil Jozf Karol Szymanski* and Salh Balidh School of Mining and Ptrolum Enginring, Univrsity of Albrta, Edmonton, Canada *Corrsponding author Raymond S. Suglo Univrsity of Mins and Tchnology, Tarkwa, Ghana Stfan Planta Laval Univrsity, Qubc, Canada Abstract: Excavation mthods dpnd on th rock conditions, location, tc. This papr invstigatd th pntration of an xcavator blad into soil. Finit lmnt modlling using th ABAQUS softwar and analytical mthods wr usd to prdict th horizontal forcs du to blad movmnt with varying soil paramtrs such as friction angl, cohsion cofficint, and angl btwn soil and blad. Th rsults obtaind from th numrical and analytical modls compar favourably with ach othr in th prdiction of soil cutting rsistanc. Th dpth of soil, intrnal friction angl and cohsion cofficint wr found to b dirctly rlatd to th cutting rsistanc of soil. Kywords: cutting rsistanc; finit lmnt; soil; friction angl. Rfrnc to this papr should b mad as follows: Szymanski, J.K., Balidh, S., Suglo, R.S. and Planta, S. (2011) Dtrmination of th cutting rsistanc modl of soil, Int. J. Mining and Minral Enginring, Vol Biographical nots: Jozf Karol Szymanski is a Profssor of Mining Enginring and consultant mining nginr with ovr 35 yars rsarch xprinc in slurry transportation, surfac mining systms simulation, rock nginring, matrials handling and surfac and undrground min dsign. Th rsults of his publications includ ovr 250 publications, numrous prsntations, two manuscripts and four patnts. Prsntly, h is a Prsidnt of J.Z. & S. Consulting Inc., a consulting company and concurrntly holds th appointmnt of Profssor of Mining Enginring at th Univrsity of Albrta. Salh Balidh compltd his MSc dgr in Mining Enginring from th Univrsity of Tarbiat Modars in H was a Mmbr of a Faculty at Copyright 2011 Indrscinc Entrpriss Ltd.

2 Dtrmination of th cutting rsistanc modl of soil 221 Sahand Univrsity of Tchnology from 2004 to H is currntly a PhD studnt at th Univrsity of Albrta, Edmonton, Canada. His aras of rsarch ar rock mass and its post failur bhaviour, bhaviour of undrground structurs subjctd to arthquaks and slop stability analysis. H dvlopd a powrful softwar that can prob continually th stability of slops in opn pit mins. Raymond S. Suglo holds a PhD dgr in Mining Enginring from th Univrsity of Albrta, Edmonton, Canada. H has ovr 27 yars of profssional xprinc in taching, rsarch and undrground mining oprations. Prsntly, h is an Associat Profssor and th Dan of Postgraduat Studis at th Univrsity of Mins and Tchnology, Tarkwa, Ghana. His rsarch aras ar min vntilation and safty nginring, simulation of mining systms, surfac and undrground min planning and dsign, mining laws and nvironmntal managmnt issus. H has to his crdit 43 publications. H is a Mmbr of SME, CIM and Ghana Institution of Enginrs (GhIE). Stfan Planta rcivd his MA (1973) and PhD (1976) at th Wroclaw Univrsity of Tchnology in Wroclaw (Poland). H has ovr 20 yars working, taching and rsarch xprinc in th mining industry (Poland, Franc, Algria and Canada). In 1989, h joind th Laval Univrsity whr h is currntly a Profssor. H tachs undrground mining mthods, undrground mining projct, hygin and safty. His rsarch aras includ undrground mining: mining mthods, mining quipmnt, or dilution and min conomics. H is a mmbr of CIM, SME and Ordr ds Ingéniurs du Québc. 1 Introduction It is rquird to xcavat soil in all civil constructions, roads and mining projcts. Excavation mthods diffr according to th rock conditions, costs, location and industrial limits. Goscinc nginring has bn usd to invstigat diffrnt typs of xcavation mthods for many yars. For xampl, drilling and blasting, mchanical xcavating machins such as road hadrs, Tunnl Boring Machins (TBMs), shovls and dozrs ar common rock braking and matrials handling quipmnt that ar usd in svral projcts (Thuro, 1997; Thuro and Plinningr, 2003). Drilling and blasting mthods ar mainly usd in hard rock conditions. Road hadrs ar usful in soft to mdium strngth rocks. TBMs and shilds ar usd in vry soft to hard rock conditions (Bilgin, 2003; Thuro and Plinningr, 2003). Shovls and dozrs can b usd to frly dig or xcavat vry soft and wathrd rock or soil. Th prformanc of all th aformntiond quipmnt dpnds mainly on th cutting conditions. Thus, invstigation of blad pntration in soil will dtrmin th fficint opration of dozrs and shovls. Th horizontal rsistanc forc is an important paramtr in dtrmining th blad pntration condition and th ovrall prformanc of th xcavation machinry. Thr hav bn many invstigations to dtrmin th cutting rsistanc forc of th blad in diffrnt typs of soils. Som invstigations hav prdictd soil cutting rsistanc using mpirical mthods whil othrs usd analytical mthods. For xampl, Zlnin t al. (1986), Hmami t al. (1994), Zhang and Kushwaha (1995) usd an xpandd mpirical formula for prdicting soil cutting rsistanc. But th mpirical formula usd did not tak into considration gomchanical paramtrs such as intrnal

3 222 J.K. Szymanski t al. soil friction angl and soil intrnal cohsion. Also, th quation is mainly applicabl to spcial kind of quipmnt and may lad to mislading rsults if usd for all typs of quipmnt in various rock conditions. For xampl, th quations that hav bn dtrmind for agricultural tools cannot b usd for dozrs if th tools and ground conditions ar diffrnt. Th analytical soil prdiction formula has bn invstigatd mor oftn than th mpirical formula. For xampl, McKys and Ali (1977), Toro (1980) and Kushwaha t al. (1993) dvlopd analytical rlations in thir work. In this papr, othr analytical formula hav bn usd to prdict th cutting rsistanc modl of soil. Ths rlations ar basd on quilibrium of forcs. Th friction angl and cohsion cofficint of soil hav major rols in th analytical rlations. 2 Analytical mthod of stimating cutting rsistanc Th mthod illustrats th distribution of forcs during tool pntration in soil. Th major part of th mthod is basd on th forcs in quilibrium. Figur 1 shows th rsulting forcs whn a cutting wdg initially pntrats into a block of soil horizontally and is gradually raisd to brak through th block, whil Figur 2 shows th maximum forcs acting along th sharing plan of th block of soil. Th advantag of using this mthod of dtrmining th cutting rsistanc is that it is drivd by balancing all th applicabl forcs in both dirctions and it is fr of momnts of diffrnt forcs. Figur 1 Forcs acting on th block of soil whn it is slightly raisd Th following nomnclatur is usd: S N : Normal soil prssur on cutting tool surfac S T : Tangnt soil prssur on cutting tool surfac β: Angl of inclination of cutting forc φ: Intrnal friction angl C: Cohsion cofficint of soil α: Cutting angl φ : Extrnal angl of friction btwn th cutting tool surfac and soil N: Normal forc N 1 : Rsultant of th normal forc and th xtrnal forc of friction

4 Dtrmination of th cutting rsistanc modl of soil 223 ξ: Angl btwn th cutting forc and raction, N 1 S 0 : Sharing forc T: Shar strngth of th soil σ n : Normal strss on cutting surfac W s : Horizontal forc of th cutting rsistanc A: Ara of cross sction of th block of soil A s : Ara of cross sction of th soil in sharing plan d: Dpth of pntration (m) l: Width of cutting wdg (m) From Figur 1, quations (1) and (2) can b dducd: π ς = α + β + ϕ 2 (1) S = N cos ζ and S = N sin ζ. (2) T 1 N 1 From Figur 2, quation (3) can b dducd: S = S + S = S + N (3) T 0 Ntgϕ 0 1tgϕ sin ς. Figur 2 Maximum forcs acting along th sharing plan of a soil block By quating th forcs acting along th sharing plan, quations (4) (6) ar obtaind: N cosς = S + N tgϕ sinς (4) S0 = N1(cosς tgϕsin ς) (5) N1cos( ζ + ϕ) S0 = = AT s. (6) cosϕ

5 224 J.K. Szymanski t al. Figur 3 shows th fr body diagram of forcs acting at th tip of th cutting dg. From Figur 3, th ratio of W s and N 1 can b dtrmind as: W N Figur 3 s 1 sin( α + 2 ϕ ) =. (7) cosϕ Fr body diagram of forcs acting at th tip of th cutting dg Thrfor quation (6) bcoms: S 0 Ws cosϕsin( α + β + ϕ + ϕ) =. sin( α + 2 ϕ )cosϕ (8) Th forcs on th othr sid may b rprsntd by: S AT = (9) sin β 0. Thrfor, th shar strss can b dtrmind using quation (10): Ws cosϕsin βsin( α + β + ϕ + ϕ) T =. Asin( α + 2 ϕ )cosϕ (10) For dtrmining sharing plan angl, th first drivativ of T with rspct to β should b qual to zro, so: dt 0 dβ = (11) π ( α + ϕ + ϕ) β =. (12) 2 Th horizontal rsistanc of th cutting rsistanc can b calculatd using ithr quations (13) or quations (14) and (15): W s = Aτ sin( α + 2 ϕ )cosϕ 2 cosϕcos [0.5( α + ϕ + ϕ)] (13)

6 Dtrmination of th cutting rsistanc modl of soil 225 or dl( σ tgϕ + c)sin( α + 2 ϕ )cosϕ W = s n 2 cosϕcos 0.5( α ϕ ϕ) [ + + ] 2 dl( σ ntgϕ + c)sin( α + 2 ϕ)cosϕ Ws =. cosϕ 1 cos( αϕ ϕ) [ + + ] (14) (15) 2.1 Effct of tool s cutting angl on horizontal forc Th horizontal cutting rsistanc was dtrmind for various cutting angls, and th rsults ar shown in Figur 4 by kping th othr paramtrs constant in th quations. A summary of th usd paramtrs is givn in Tabl 1. Th rsults show that th cutting rsistanc forc and cutting tool angls hav xponntial rlationship with ach othr. Tabl 1 Summary of usd paramtrs Intrnal friction angl Cohsion cofficint (kpa) Extrnal friction angl Ara of cross sction (A, m 2 ) Dnsity (kn/m 3 ) Figur 4 Variation of horizontal cutting rsistanc with cutting angl 2.2 Effct of intrnal friction angl on horizontal forc Horizontal cutting rsistanc was dtrmind for various intrnal friction angls, and th rsults ar shown in Figur 5. Th rsults show that cutting rsistanc forc and intrnal friction angl hav an xponntial rlation with ach othr. From Figurs 4 and 5, it can b sn that th ffct of intrnal friction angl on cutting rsistanc is highr than that of th cutting angl on cutting rsistanc.

7 226 J.K. Szymanski t al. Figur 5 Variation of horizontal cutting rsistanc with intrnal friction angl 2.3 Effct of xtrnal friction angl on horizontal forc Horizontal cutting rsistanc was calculatd for various xtrnal friction angls and th rsults ar shown in Figur 6. Th rsults show that cutting rsistanc forc and xtrnal friction angl ar linarly rlatd up to a critical limit, and aftr that th rlationship is vry unprdictabl. This angl is not constant and dpnds on othr paramtrs such as th intrnal friction angl of soil. Horizontal cutting rsistanc as a function of intrnal friction angl and xtrnal friction angl has bn calculatd in Figur 7. Th rsults show that for highr intrnal friction angls, th cutting rsistanc-xtrnal friction angl curv is shapr. Figur 6 Variation of horizontal cutting rsistanc with xtrnal friction angl

Dtrmination of th cutting rsistanc modl of soil 227 Figur 7 Variation of horizontal cutting rsistanc as a function of intrnal friction angl and xtrnal friction angl (s onlin vrsion for colours) 2.

8 Dtrmination of th cutting rsistanc modl of soil 227 Figur 7 Variation of horizontal cutting rsistanc as a function of intrnal friction angl and xtrnal friction angl (s onlin vrsion for colours) 2.4 Effct of cohsion cofficint on horizontal forc Horizontal cutting rsistanc was dtrmind for various cohsion cofficints and th rsults ar shown in Figur 8. Th rsults show that cutting rsistanc forc and cohsion cofficint ar dirctly rlatd to ach othr. Figur 8 Variation of horizontal cutting rsistanc with cohsion cofficint 3 Numrical modlling of soil cutting rsistanc In this sction, th finit lmnt mthod has bn usd to invstigat th soil cutting rsistanc. ABAQUS softwar is also usd to conduct numrical modlling of soil (Elnor and Hamilton, 2004). Th ABAQUS softwar was usd to do a 2D modlling of soil cutting to compar with th rsults of th analytical modl obtaind arlir on in this

25 12 Soil dformd during tool pntration is shown in Figur 9. Th numrical modlling usd a cutting tool with a wdg shap.

9 228 J.K. Szymanski t al. papr. Th modlld soil has an qual Mohr-Coulomb bhaviour. Th rsults of th modlld soil proprtis ar summarisd in Tabl 2. Tabl 2 Summary of modlld soil proprtis Intrnal friction angl 25 Cohsion cofficint (KPa) Elastic modulus (MPa) Poisson s ratio Dnsity (kn/m3) Soil dformd during tool pntration is shown in Figur 9. Th numrical modlling usd a cutting tool with a wdg shap. Th cutting rsistanc was calculatd using th ABAQUS softwar aftr modlling and compard with analytical rsults. Th paramtrs on cutting rsistanc of soil wr also invstigatd by changing th paramtrs in th finit lmnt modl. Th rsults of ths invstigations ar prsntd in th nxt sctions. Figur 9 Soil dformd by tool pntration (s onlin vrsion for colours) 3.1 Shar plan and yild ara Figur 10 shows th yild rang during tool pntration. Th plastic strain and shar strss distributions ar shown in Figurs 11 and 12 rspctivly. From Figurs 10 and 12, th dirction of shar plan is compatibl with th assumd shar plan in th analytical rlation shown in Figur 1. Thus, th assumd shar modl in th analytical mthod is valid. Figur 10 Distribution of th yild ara during tool pntration (s onlin vrsion for colours)

Dtrmination of th cutting rsistanc modl of soil 229 Figur 11 Plastic strain distribution rang aftr tool pntration (s onlin vrsion for colours) Figur 12 Shar strss distribution

2 Effct of dpth on horizontal forc On of th ffctiv paramtrs on th horizontal rsistanc forc is th dpth of th soil abov th cutting tool.

10 Dtrmination of th cutting rsistanc modl of soil 229 Figur 11 Plastic strain distribution rang aftr tool pntration (s onlin vrsion for colours) Figur 12 Shar strss distribution aftr tool pntration (s onlin vrsion for colours) 3.2 Effct of dpth on horizontal forc On of th ffctiv paramtrs on th horizontal rsistanc forc is th dpth of th soil abov th cutting tool. This paramtr is on of th variabls in quation (15). In th analytical mthods, th soil was modlld with tool pntration dpths of 1 m, 0.7 m and 0.4 m rspctivly, and th rsultant horizontal rsistanc forc calculatd for ach dpth (s Figur 13). Figur 13 Dformation of soil aftr tool pntration for 1, 0.7 and 0.4 m dpth of soil (s onlin vrsion for colours)

11 230 J.K. Szymanski t al. Figur 14 shows th calculatd cutting rsistanc for ach soil dpth using quation (15) in th analytical modl as wll as th rsults of th numrical modlling using ABAQUS for ach dpth. Th rsults show that th cutting rsistanc is linarly rlatd to th dpth of soil cut. Also, th analytical rsults strongly corrlat with thos obtaind using numrical modlling. Howvr, mor scnarios ar rquird (in furthr rsarch) to fully confirm th corrlation btwn th two mthods. 3.3 Effct of th intrnal friction angl on horizontal forc Th intrnal friction angl is on of th critical paramtrs that control th mchanical bhaviour of soils. Thrfor, th influnc of this variabl was invstigatd in both numrical and analytical modls. Th rsults ar shown in Figur 15. It shows that th intrnal friction angl is dirctly rlatd to th cutting rsistanc of soil in both modls. Figur 14 Horizontal forc of cutting rsistanc for 1, 0.7 and 0.4 m dpth of soil (s onlin vrsion for colours) Figur 15 Variation of horizontal forc with intrnal friction angl (s onlin vrsion for colours)

12 Dtrmination of th cutting rsistanc modl of soil Effct of th cohsion cofficint on horizontal forc Th ffct of cohsion cofficint on horizontal forc is anothr paramtr that was xamind in this work. Th rlationship btwn cohsion cofficint and cutting rsistanc is shown in Figur 15 for numrical and analytical mthods. From Figur 16, thr is a linar rlationship btwn cohsion cofficint and cutting rsistanc in th analytical modl, but th rlationship btwn thm is not vry linar in th numrical modl. Again, mor scnarios ar rquird (in furthr rsarch) to fully confirm th corrlation btwn th two modls. Figur 16 Variation of horizontal forc with cohsion cofficint (s onlin vrsion for colours) 4 Conclusions From th analysis in this papr, it can b concludd that th rsults obtaind from th numrical and analytical modls compar favourably with ach othr in th prdiction of soil cutting rsistanc. Th analytical mthod, which is asy to us, can stimat cutting rsistanc with an accptabl lvl of tolranc. Furthr invstigations (in futur rsarchs) ar rquird to dtrmin whthr th analytical modl is applicabl in all situations or only undr spcial conditions. Mor scnarios ar rquird to fully confirm th corrlation btwn th two modls. Rfrncs Bilgin, N. (2003) Drill ability prdiction in rotary blast hol drilling, Intrnational Mining Congrss and Exhibition, Turky, MCET, pp Elnor, M.A. and Hamilton, R. (2004) Simulation of soil-blad intraction for sandy soil using advancd 3D finit lmnt analysis, Soil and Tillag Rsarch, Vol. 75, pp Hmami, A., Goult, S. and Aubrtin, M. (1994) Rsistanc of particulat mdia to xcavation: application to buckt loading, Int. Journal of Surfac Mining and Rclamation, Vol. 8, pp

13 232 J.K. Szymanski t al. Kushwaha, R.L., Chi, L. and Shn, J. (1993) Analytical and numrical modls for prdicting soil forcs on narrow tillag tools, Canadian Agricultural Enginring, Vol. 35, No. 3, pp Mckys, E. and Ali, K.O.S. (1997) Th cutting of soil by narrow blads, Journal of Trramchanics, Vol. 14, No. 2, pp Thuro, K. (1997) Drillability prdiction: gological influncs in hard rock drill and blast tunnling, Gol. Rundsch, Vol. 86, pp Thuro, K. and and Plinningr, R.J. (2003) Hard rock tunnl boring, cutting, drilling and blasting: rock paramtrs for xcavatability, Procdings of 10th Intrnational Socity for Rock Mchanics (ISRM) Congrss, pp Toro, G. (1980) Ciagnikow maszyny do robot zimnych, Wydawnictwa Politchniki Warszawskij, Warszawa Zlnin, A.N., Balovnv, V.I. and Krov, I.P. (1986) Machins for Moving th Earth: Fundamntals of th Thory of Soil Loosning, Modling of Working Procsss and Forcasting Machin Paramtrs, Balkma, A.A., Th Nthrlands, Rottrdam, p.555. Zhang, J. and Kushwaha, R.L. (1995) Hard a modifid modl to prdict soil cutting rsistanc, Soil and Tillag Rsarch, Vol. 34, pp

4.2 Design of Sections for Flexure

4.2 Design of Sections for Flexure 4. Dsign of Sctions for Flxur This sction covrs th following topics Prliminary Dsign Final Dsign for Typ 1 Mmbrs Spcial Cas Calculation of Momnt Dmand For simply supportd prstrssd bams, th maximum momnt