Uxinzelelo kwimijelo emide lubunjwa yi (umz. 1):
Umz. 1. Amandla oxinzelelo asebenza kwitonela
a) uxinzelelo oluthe nkqo P phezu kwencam, olubizwa uxinzelelo lwe-crest,
b) yoxinzelelo oluthe tye S, olubizwa ngokuba luxinzelelo olusecaleni,
c) iimpendulo ezisezantsi A, ezibizwa uxinzelelo lwesiseko.
Ubukhulu boxinzelelo lomhlaba emseleni buhamba ngemida ebanzi kakhulu. Ekuqaleni, ngexesha lokuvulwa komseleni, uxinzelelo lweentaba luphantsi ngokuthelekisa kwaye lusuka ku 0 ukuya ku 0,50 kp/cm2, kodwa emva kokuvulwa luyanda luze lusuke ku 0,8 ukuya ku 12,0 kp/cm2, kuxhomekeka kuhlobo lomhlaba nakwiimpawu zawo zomzimba, ukuphakama kweengqimba ezingaphezu komseleni nakubungakanani beentshukumo emhlabeni ezivela ngenxa yoxinzelelo lweengqimba ezingasentla. Ngenxa yokuxhomekeka kwizinto ezahlukeneyo, ukumiselwa koxinzelelo lweentaba emseleni kunzima kakhulu, ngoko ke ngendlela yethiyori akunakumiselwa ixabiso elichanileyo loxinzelelo lomhlaba, koko kuphela elikufuphi. Ngokuchasene nefuthe loxinzelelo lomhlaba kwiprofayile yomseleni kukho ukuxhathisa kwangaphakathi komhlaba. Ukuba umhlaba apho umseleni wenziwa khona uquka ilitye eliqinileyo nelixineneyo, uxinzelelo kwiprofayile yomseleni alubalulekanga, kuba ubunzima beengqimba ezingaphezu komseleni buthwalwa luxinzelelo lokucheba lwaloo litye liqinileyo. Kwimeko enjalo akukho mfuneko yokwenza umaleko womseleni okanye inkxaso ngexesha lokuvulwa komseleni, yaye ke kuyangasafuneka nokumiselwa koxinzelelo lomhlaba kwiprofayile yomseleni.
Kwimigxobhozo engadityaniswanga kakuhle nenokuguguleka ngokulula, uxinzelelo olubangelwa bubunzima bamaleko angasentla kwiprofayili yetonela lunokugqitha amandla aloo matye, nto leyo ekhokelela ekuqhekekeni komhlaba nakwiinguqu ezinamandla kwiprofayili yetonela. Kwiimeko ezinjalo kufuneka kusetyenziswe inkxaso ngexesha lokugrumba itonela, emva koko kwenziwe umaleko wetonela oya kumelana noxinzelelo lwentaba aze uludlulisele ngefundamenti ukuya kumaleko asezantsi.
Kwimihlaba edityanisiweyo, ukuxhathisa kwangaphakathi kubandakanya ukudibana nokukhuhlana, kanti kumhlaba ongadityaniswanga kubandakanya kuphela ukukhuhlana ngaphandle kokudibana. Noko ke, ngenxa yokuba ixabiso lokudibana litshintsha phantsi kwempembelelo yokufuma, kwanokumaleka komhlaba okwenziwe ziintlobo ezahlukeneyo, ukudibana akuthathelwa ngqalelo njengokuxhathisa kwangaphakathi, ngoko kwanakwimihlaba edityanisiweyo kubalwa kuphela ukukhuhlana kwangaphakathi. Ngenxa yoko, kuzo zombini ezi meko zokugqibela kufuneka kubekho umaleko wetonela, nto leyo ethetha ukuba kufuneka kumiselwe uxinzelelo lomhlaba kwitonela.
Ukumisela ubungakanani boxinzelelo lomhlaba kwitonela kukho ezi ngcinga zilandelayo:
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Ingcinga yokuba uxinzelelo lomhlaba lukhula ngokomlinganiselo nobunzulu
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Ingqikelelo esekelwe kwimithetho yokulingana kwemizimba ethe nkcitho
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Ingcinga ngokusekwa kwebhodi yokukhulula umthwalo emhlabeni
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Ingcinga esekelwe kwimithetho ye-elasticity.
Uqikelelo lokuba uxinzelelo luyanda ngokomlinganiselo nobunzulu
Ngokwesi sithathwa, kuphahla lwetonela (umz. 2) kusebenza uxinzelelo lwencopho P ngenxa yobunzima bomhlaba kubude bonke obungaphezulu kwetonela ukuya kumphezulu womhlaba, nakububanzi betonela embiweyo b. Ngoko ke, uxinzelelo lwencopho ngu
P = γ bt [Mp/m]
apho γ bubunzima bomthamo weengqimba zomhlaba ezingentla kwetonela [Mp/m3], t ukuphakama kweengqimba zomhlaba ezingentla kwetonela [m].
Le ngcinga yamkelwa kuphela kwiimeko ezikhethekileyo, njengomzekelo xa umhlaba ongaphezulu kwetonela wenziwe ludaka, olunengeniso yangaphakathi phantse ingekho, okanye ngumhlaba onxulumene nowangenxulumaniyo kumanzi angaphantsi komhlaba, xa ukuxhathisa komhlaba kuncinci kunempembelelo yobunzima bomhlaba.
Ezi meko zinokubakho zinqabile ekusebenzeni kwaye ziphathwa njengeemeko ezikhethekileyo. Kuzo zonke ezinye iimeko, xa kunokubalwa ngokuxhathisa kwangaphakathi komhlaba, ukumiselwa koxinzelelo lomhlaba kwiitunela ngolu cebo akulungiseki, kuba lunika uxinzelelo olukhulu kakhulu kunolo lokwenyani.
Umz. 2. Ukumiselwa koxinzelelo lomhlaba kwituneli phantsi kwengcinga yokuba uxinzelelo luyanda ngokomlinganiselo nobunzulu
Uqikelelo olusekelwe kwimithetho yokulingana kwemizimba echithakeleyo
Sl. 3. Ukumiselwa koxinzelelo lomhlaba kwitonela ngokucingela okusekelwe kwimigaqo yebhalansi yemizimba ewayo
Ngokwesi siseko kujongwa umhlaba owomileyo, ophothiweyo, yaye kwamkelwa ukuba uxinzelelo kwigophe letunela luncinci kunobunzima beprism ABA’B’ ngenxa yempembelelo yamandla okukhuhlana kwimiphezulu ethe nkqo AA’ kunye BB’ (umz. 3).
Kule ngcinga kusekelwe iindlela ezininzi zokubala uxinzelelo kwisithsaba setonela, ezinjengezo zika-Forcheimer, Bierbaumer no-Engesser.
Ubunzima obupheleleyo bomhlaba ongaphezulu kwevault yetonela ngu W= γ bt, kodwa iprism ABA’B’ ayisayi kukwazi ukutyibilika ngokukhululekileyo iye ezantsi, kuba olu tyibiliko luya kuphikiswa kukungqubana kwezinto kumphezulu AA’ kunye no BB’. Ukuba o yi-engile yokungqubana kwangaphakathi komhlaba ongaphezulu kwevault yetonela, i-coefficient yokungqubana ngu tgo, kwaye uxinzelelo oluqhelekileyo kumphezulu wokungqubana luyinyani ngumkhosi osecaleni E, uxinzelelo lomhlaba olusebenzayo kumphezulu AA’ kunye no BB’. Ngoko ke kumphezulu ngamnye wale nto kusebenze umkhosi wokungqubana
Q = Ea tg_ϕ._
Uxinzelelo P kwisigqubuthelo setonela, uxinzelelo lwencopho, ngu
Uxinzelelo olusebenzayo lomhlaba lubalwa ngokweRankine
Ea = ½ γt2 tg2(45o – ϕ/2)
Ukumisela uxinzelelo lomhlaba kwitonela ngokwale ngcinga kwenziwa kunqabile yaye kuphela kwezinye iimeko, njengomzekelo xa ukuphakama kweemaleko zomhlaba ngaphezu kwetonela kuncinci, ukuze kungabikho ndlela yokwakheka kwevouthe yokukhulula umthwalo.
Ingcinga ngokusekwa kwebhodi yokukhulula umthwalo
Ngale ndlela, kuwo nawuphi na umhlaba odibeneyo nowangadibenanga, ngaphandle kodaka, ngaphezulu kwetonela kwakheka umqadi wokukhulula umthwalo, ukuze kwiprofayili yetonela kusebenze kuphela izinto ezingaphantsi kwaloo mqadi, logama umqadi ngokwawo ugcinwa kulungelelwano ngenxa yesenzo se-arc, nto leyo ebonakaliswe ziimvavanyo kumhlaba oyisanti okhululekileyo. Ukumisela uxinzelelo lomhlaba kwitonela ngokwale ngcinga kukho iindlela ezininzi, phakathi kwazo ezaziwa kakhulu yiKommerell neProtođakonov. Ngendlela kaKommerell kwamkelwa ukuba umqadi wokukhulula umthwalo unomumo we-semi-ellipse, kanti ngendlela kaProtođakonov unomumo weparabola.
Indlela kaKommerell yesiqingatha-se-ellipse yoxinzelelo
Ngale ndlela kucingelwa ukuba ukuphakama kwe-arch yokukhulula umthwalo h kuxhomekeke kububanzi betonela kunye ne-engile yokungqubana kwangaphakathi komhlaba apho itonela igrunjwa khona (sl. 4). Ukuphakama kwe-arch yokukhulula umthwalo h kunokumiselwa ngokusekelwe kule fomula:
h = 100_a_/p
apho a kukuhlala phantsi kwenkxaso ukusuka ekuqaleni kokugrunjwa kwetonela de kugqitywe ukwakhiwa kodonga lwe-tonela, p kukukhululeka komhlaba okungapheliyo.
Fig. 4. Ukumiselwa koxinzelelo lomhlaba kwitonela ngokwendlela yesiqingatha-se-ellipse yoxinzelelo
Xa iimeko ziluncedo kwamkelwa a = 10 – 15cm, xa zingalunganga a = 15 – 40cm, xa zingalunganga kakhulu a = 40 – 70cm.
Ukuxhathisa okusisigxina komhlaba p kumiselwa kumhlaba ogrunjiweyo wetonela nge-% emva kokugrunjwa nokuxinwa kwakhona. Amaxabiso p akwiimida ezinikiweyo kwitheyibhile 1.
Nangona kunjalo, nangona le fomula ingentla isetyenziswa rhoqo kakhulu ekusebenzeni, ithathwa njengengahambelani nenyani. Ukuzinza a kunalo ixabiso elipheleleyo, koko kumalunga nezinto ezahlukeneyo kwinto enye ngokohlobo lwesakhiwo esingezantsi. Ukuba isakhiwo esingezantsi senziwe ngentsimbi, ukuzinza kuncinci, ukuba senziwe ngomthi ukuzinza kukhulu. Kwiiprofayile eziqhelekileyo zetonela kwiindlela zikaloliwe nakwiindlela, kuthatyathwa ukuba kubude bomaleko womhlaba ngaphezu kwetonela t > 20 m ukuphakama kwedome yokuthomalalisa h=20 m.
Uxinzelelo olusecaleni_. NgokukaKommerell, uxinzelelo olusecaleni luvela ngenxa yesenzo sobunzima beprizim yomhlaba ABC (umz. 4), ethintelwe emacaleni ngumphezulu oshenxayo AC nenqwelomoya ethe nkqo yetonela AB, ngoxa phezulu ithwele ubunzima beprizim yomhlaba CBG. Apha kuqwalaselwa ukuba iprizim yomhlaba esebenzayo ithintelwe phezulu ngumphezulu othe tye CB kwinqwelo yencopho yendawo yokugoba yetonela
Itheyibhile 1. Amaxabiso asondeleyo omhlaba p kwi %
Kuba umgangatho AB uthe nkqo, umgangatho CB uthe tye, kuyamkelwa ukuba kukho imeko ka-Rankine yoxinzelelo lomhlaba, yaye isalathiso soxinzelelo lomhlaba olusebenzayo E sithe tye. Ngokuka-Rankine, ithambeka lomphezulu wetyibiliko AC ngokubhekiselele kwihorizontal likwi-engile α=45o+ϕ/2, uxinzelelo lomhlaba olusebenzayo Ea luthi
Ea = ½ _γh_2tg2(45o-ϕ/2),
apho γ bubunzima bomthamo womhlaba kwi Mp/m3, h bubude bodonga oluxhasayo kwi m, ϕ yi-engile yokungqubana kwangaphakathi komhlaba.
Njengoko iprism yomhlaba esebenzayo ABC ilawulwa ukusuka phezulu ngobunzima beprism CBG, kulo mzekelo kuya kuba kubude betonela h’
Ea = ½ γ h’ 2tg2(45o-ϕ/2),
apho γ1 = γ + 2p/h’
apho p = Q/CB = Q/h’tg(45o- ϕ/2)
Ubunzima Q bufumaneka njengomahluko wobunzima W yesiqingatha se-ellipse yoxinzelelo CEF kunye nobunzima W1:Q = W – W1.
Ubunzima W bufunyanwa kummandla A wekota ye-ellipse nakubunzima bomhlaba ngexesha, γ, W = Aγ. Ummandla A ufumaneka ngokusekelwe kwibala le-ellipse: A = h·e·π/4
Xa sifaka ixabiso lika p kwi-equation ka Ea sifumana:
Ea = ½ γ h’2 tg2 (45o-ϕ/2) + Q tg(45o-ϕ/2).
Uxinzelelo lwe-crest. Kuba i-vault yokukhulula umthwalo ilingana ngokomlinganiselo kumgca othe nkqo, ngoko unako ukubalwa uxinzelelo lwe-crest kwisiqingatha seprofayili yetonela. Ubunzima W1 beprizim yomhlaba BEFG kubude betonela 1,00 m buzi:
W1 = (z+h)/2 · b/2 · 1,00 · γ
Kule nxaki yonke into iyaziwa ngaphandle kwe z, esiyimisela ngokusekelwe kwinxaki yesiphaluka se-ellipse (sl. 5): b2x2 + a2y2 = b2a2. Kwimeko yethu b=e; a=h; x=z;
Sl. 5. Ukumiselwa koxinzelelo lwesithsaba setonela ngendlela ye-semi-ellipse yomthwalo
Umz. 6. Uxinzelelo olusisiseko p phantsi kwenkxaso
Uxinzelelo lwesiseko. Kuba kucingelwa ukuba uxinzelelo lwesiseko A lulingana noxinzelelo lwencopho P, ngoko ubungakanani balo buchaziwe ngoko.
Ukuba iprofayile yetonela ine-arch esezantsi, uxinzelelo ezantsi kwetonela p ngu: p = P/(b·1,00m) [Mp/m2].
Kodwa ukuba oku kuqinile kwaye kunomthamo wokuthwala owaneleyo, uxinzelelo lwencopho P ludluliselwa ziinkxaso ezinobubanzi d ukuya emhlabeni (sl. 6), ngoko ke uxinzelelo lwesiseko phantsi kweenkxaso luthi: p = P/(2d·1,00m) [Mp/m2].
Kuyaphawulwa ukuba kule meko kuyimfuneko ukwenza uphononongo lomhlaba kunye nokumiselwa komthamo wokuthwala nokuhlala komhlaba, kuba kuye kwenzeka ukuba umthamo wokuthwala komhlaba ube mncinane kunoxinzelelo lwesiseko, nto leyo ekhokelele ekuguqukeni kokugqunywa kwetonela nasekuhlaleni kwayo yonke itonela.
Ingcinga esekelwe kwimigaqo ye-elasticity
Kutshanje kuye kwavela ingcinga entsha yokujonga umhlaba njengomzimba one-elasticity ofanayo one-isotropic, apho kunokusetyenziswa khona imithetho ye-elasticity. Ngokwale ngcinga, i-axes ze-elastic zomhlaba zichazwa yi-modulus yawo ye-elasticity E kunye ne-Poisson coefficient µ exhomekeke kwiimpawu ezibonakalayo zomhlaba. Nangona kunjalo, eneneni umhlaba awunalo i-isotropy, koko ungu masa we-anisotropic, amaxabiso e-modulus E kunye ne-coefficient µ atshintsha ngobunzulu. Noko kunjalo, nangona le kuphambuka ikhona, ukusetyenziswa kwethiyori ye-elasticity ekumiseleni uxinzelelo lomhlaba kunomdla omkhulu wesayensi kwaye kunika amathuba ophando oluzayo.
Ukuvavanywa kozinzo lwesigqubuthelo setonela phantsi kwesenzo soxinzelelo lomhlaba
Ukuvavanya uzinzo lwe-lining yetonela kukhethwa umnqamlezo we-lining, apho kuluncedo ukusebenzisa imizekelo yeetonela ezazakhiwe ngaphambili phantsi kweemeko ezifanayo nezikule meko, ezazihlale zikwimeko entle, okanye ke umnqamlezo we-lining yetonela umiselwa ngenye indlela ye-empirical (sl. 7a). Umnqamlezo okhethiweyo we-lining yetonela wahlulwa ube ziilamella ezinobubanzi obulinganayo kangangoko Δs. Kwelinye nelinye ilamella kumiselwa uxinzelelo oluthe nkqo nolusecaleni, kwakunye nobunzima belamella ngokwalo.
Uxinzelelo oluthe nkqo PG kwilamela lobude betonela 1,00 m (umz. 7a) lufunyanwa ngokusekelwe kwifomula:
PG = (y1+y2)/2 · Δ_x_·1,00·γ
Sl. 7. Ukumiselwa koxinzelelo lomhlaba emseleni ngokwendlela kaKommerll
Uxinzelelo olusecaleni luqulunqwa luxinzelelo lomhlaba Eh, kwiprofayili yetonela enobude h’ kunye noxinzelelo Ea ngenxa yesenzo somthwalo Q
Eh’ = ½ γ h’2 tg2 (45o-ϕ/2); Ea = Q tg(45o-ϕ/2).
Ukumisela uxinzelelo olusecaleni Eh kwiilamella ezithile zembotyi kubekwa idayagram yoxinzelelo olusecaleni (7a) ngokusekelwe kwizibalo:
Amandla PG kunye ne-Eh asebenza kwiiasi zeelamela ezihambelanayo.
Ukongezelela, kumiselwa nobunzima belamela lomaleko PZ, elisebenza kumbindi walo wobunzima, kuze kufunyanwe iresultanti R yawo onke amandla kwilamela elinikiweyo (umz. 7b). Ngale ndlela kumiselwa iresultanti R1, R2, R3 yawo onke amalela (umz. 8a), adityaniswa kwisicwangciso samandla (umz. 8b), kuze kufumaneke iresultanti Rn. Emva koko, ukusuka kwi-pole engakhethiyo O kutsalwa imiqadi kuze kuzotywe umgca wokuqala wokuxhasa ac. Ngokomqathango wokuba ivault ikwimeko yolungelelwano ukuba uxinzelelo oluthe tyaba lwevault H, iresultanti yoxinzelelo lomhlaba kwitonela R_n kunye noxinzelelo lwesiseko A zidibana kwindawo enye, sifumana indawo yokudibana S. Ukuba siyayidibanisa le ndawo nombindi wokuqhagamshelwa kwevault kwisihlalo sayo, sifumana umgca woxinzelelo olutsha lwesiseko A1. Ukuba sidibanisa amandla Rn, A1 no H kwisicwangciso samandla esitsha (umz. 8c), sifumana ubukhulu be H kunye ne-pole entsha O1 apho sikhupha kuyo imiqadi emitsha kunye nomgca wesibini wokuxhasa ac’.
Sl. 8 Isicwangciso samandla kunye nomgca oxhasayo woxinzelelo lomhlaba kwitunela
Ngokwelayini entsha yokuxhasa efunyenweyo kulungelelaniswa iprofayile enqamlezileyo yomgquba womseleni, yaye kuyakhiwa ilayini yokuxhasa kwakhona, ukuba kuyimfuneko, nangesihlandlo sesithathu. Umgudu kukwamkela uhlobo olunjalo lomgquba womseleni, apho i-axis yawo ihambelana nelayini yokuxhasa. Kule meko kulawula kuphela iingcinezelo zoxinzelelo kumgquba. Uxinzelelo lwesikhamiso oluvela kuyo nayiphi na indawo enqamlezileyo n – n womgquba womseleni (sl. 8), lufunyanwa kwifomula
apho N yinxalenye eqhelekileyo yesiphumo Rn kwicandelo lokufumba n – n , elifunyanwa kwiplani yamandla yelo candelo; d bubukhulu bokugquma kwetuneli kwicandelo n – n; e kukungabikho embindini kwamandla okuhlasela N kwelo candelo linye.
Uxinzelelo lokucinezela σ kufuneka lube luncinane kunoxinzelelo oluvumelekileyo lwengubo. Kwii-arch zeetonela ezenziwe ngekhonkrithi eyomeleziweyo kuthathwa ukuba le ndlela ayichananga ngokwaneleyo, ngoko kunconywa indlela kaSpangerberg.