A cikin ilimin injiniyan ƙasa ana ƙayyade iyakar ɗaukar nauyin ƙasa da nauyin ƙasa da aka yarda da shi.
Ƙarfin ɗaukar kaya na iyaka na ƙasa shi ne wanda ake kaiwa a lokacin da rushewar ƙasa ta fara. Rushewar ƙasa tana faruwa ne idan nauyin da tushe yake ɗora wa ƙasa ya wuce ƙarfin ta na jure yanka. A wannan yanayin, a ƙarƙashin nauyin tushe P suna bayyana saman mafi ƙanƙantar juriya ACD da BCE – saman zamewa fig. 1, ta wurin da ƙasa ke matsewa a gefe kuma a lokaci guda ƙasar da ke sama da saman fili kusa da ginin DG da EF tana ɗagawa, yayin da tushen kansa yake nitsewa.
Sl. 1. Karyewar ƙasa ƙarƙashin tasirin nauyin tushe
Ƙarfin jure yankewa na ƙasa yana ƙaruwa da zurfin kafawa t, domin saboda nauyin layukan sama yuwuwar matsa gefe tana raguwa. Saboda haka, tushe masu zurfi suna fi wahalar jawo karyewar ƙasa, yayin da tushe masu ƙanƙanta zurfi suke da haɗarin karyewa. Haka kuma tushe masu faɗi suna fi wahalar jawo karyewar ƙasa, domin filayen zamewa suna kasancewa mafi zurfi.
Wurin ɗaukar nauyi da aka amince da shi na ƙasa shi ne wanda za a iya bari ya yi aiki a ƙasa ba tare da ya haifar da karyewar ƙasa ba a cikin mafi munin yanayi mai yiwuwa. Ana ƙayyade nauyin ƙasa da aka amince da shi bisa ƙarshen ƙarfin ɗaukar nauyin ƙasa ta amfani da ma’aunin tsaro. Girman ma’aunin tsaro ya dogara da abubuwa da dama, daga cikinsu mafi muhimmanci su ne daidaiton halayen jiki na ƙasa, yiwuwar sauyin ƙimomin abubuwan juriyar cikin ƙasa musamman haɗin kai, wanda ƙimarsa na iya bambanta sosai saboda tasirin ruwa a cikin ƙasa, sannan kuma tasirin wasu abubuwa masu yiwuwa, kamar yanayin ɗaukar nauyi (yiwuwar ɗaukar nauyi kwatsam da na dindindin), zurfin kafawa, da faɗin faifan tushe.
Ana iya ƙayyade ɗaukar nauyin ƙasa ne bisa karyewar ƙasa, wanda ke ba da iyakar ɗaukar nauyi. Iyakacin ɗaukar nauyin ƙasa yana nufin girman nauyin da ke jawo karyewa. Akwai hanyoyi biyu na ƙayyade iyakar ɗaukar nauyi bisa karyewar ƙasa, wato mafita ta lissafi da gwajin ɗora nauyi.
Maganin lissafi
Yawancin masana sun yi ƙoƙarin nemo mafita ta lissafi domin tantance iyakar ɗaukar nauyin ƙasa, bisa sanin abubuwan da ke yin tasiri da kuma bisa mabambantan zato game da yanayin karyewa. Abubuwan da ke yin tasiri su ne siffofin zahiri na ƙasa, waɗanda ake ƙayyade su ta gwaje-gwajen dakin gwaje-gwaje a kan samfurorin ƙasa da ba a taɓa lalata su ba, yanayin ruwan karkashin ƙasa, zurfin tushe, girma da siffar yankin da ake ɗora wa nauyi, haka kuma hanyar ɗorawa, wato ɗorawa daidai ko ba daidai ba, ta tsakiya ko a gefe. Zato game da yanayin karyewa sun dogara ne a kan ka’idar filastisiti da ka’idar elasticity. Duk da haka, hanyoyin zamani na tantance ɗaukar nauyin ƙasa suna dogara ne a kan ka’idar filastisiti, wadda ake haɗawa da wasu zato masu sauƙaƙawa.
A nan za mu kawo wasu sanannun hanyoyin ƙididdiga na tantance iyakar ɗaukar nauyi, wato nauyin ƙasa da aka yarda da shi.
Tsarin Prandtl-Caquota
Idan an kafa ƙafar tushe AB a zurfin t ƙasa da saman fili, a wannan zurfin ana samun matsin lamba na hulɗa p saboda nauyin tushe da kuma matsin lamba na gefe p=γt saboda nauyin ƙasa da ke sama da matakin ƙafar tushe har zuwa saman fili (sl. 2).
A ƙarƙashin tasirin kai tsaye na nauyin tushe, a lokacin da aka wuce iyakar ikon ɗaukar nauyin ƙasa, sai su bayyana faɗin saman zamewa na gaskiya AC da BC, waɗanda ke kafa kusurwa α = 45° + ϕ/2 da saman da aka ɗora nauyi a kai. Waɗannan saman zamewar suna samar da prizm ɗin ƙasa mai aiki ABC.
Hoto. 2. Filayen zamewa na siffar karkace logaritmik ƙarƙashin aikin gindin tushe da aka ɗora nauyi a tsakiya bisa Prandtl-Caquot
A ƙarƙashin matsin prism ɗin ƙasa mai aiki, ana samuwar prizmomin ƙasa masu neman tura gefe zuwa sama ADD1 da BEE1, waɗanda take ƙoƙarin tura su sama a kan saman zamewa DD1 da EE1, a kusurwar 45°-ϕ/2 da kwance. Tsakanin yankin matsin ƙasa mai aiki da na marar aiki akwai yankin yanke radiyal ACD ko BCE, inda idan aka wuce iyakar daidaito, zamewa ke faruwa a kan lanƙwasassun saman zamewa. Résal ya ƙididdige cewa saman zamewa a yankin yanke radiyal suna da siffar spiral mai logarithm, da pole a A ko B, kuma ƙa’idarsa ita ce r=r0 eπ tg_ϕ_
Don ƙayyade iyakar lodin ƙasa an yi waɗannan zato masu zuwa:
- cewa tushe yana santsi, wato ana watsi da gogayya tsakanin ƙafar tushe da ƙasa;
- da ƙarfi na yanke na ƙasa a kan saman D1M da E1N ba ya wanzuwa, wato an yi watsi da shi;
- cewa nauyin ƙasa na ƙarƙashin gindin tushe γ=0, wato ana yin watsi da tasirin nauyin ƙasa a ƙarƙashin takalmin tushe, a yankin daidaiton roba.
Tsarin Prandtl-Caquota ya ce:
Ƙarfin ɗaukar nauyin ƙasa na iyaka shi ne
Idan muka sa:
Iyakar ƙarfin ɗaukar nauyin ƙasa mai ɗaurewa ita ce qf = γtm + cm1.
Don mabambantan ƙimomin kusurwar gogayyar cikin ƙasa, ƙimomin m da m1 an ba su a cikin tebur 1.
Teb. 1. Darajar ƙimomin m da m__1 na mabambantan darajar kusurwar gogayyar cikin gida ta ƙasa
Matsin ƙasa da aka yarda da shi shi ne qa = pdozv = qf/F inda F shi ne abin tsaro. Don amfani da tsarin Prandtl-Caquot ana ɗaukar F = 4, don haka qa = qf/4.
Tsarin Terzaghi
Terzaghi ya ba da wata dabara ta rabin-empirikal don ƙididdige iyakar iya ɗaukar nauyin ƙasa a ƙarƙashin nauyin nau’in layi, murabba’i da farantin zagaye. Ya yi la’akari da tushe da aka kafa a zurfin Df ƙasa da saman fili, da faɗin B (sl. 3), sannan ya ɗauka cewa akwai gogayya tsakanin kafar tushe AB da ƙasa, wadda ke ƙin tura ƙasa a gefe, kuma saman zamewar AB da BC suna samar da kusurwar gogayyar ciki da saman da aka ɗora masa nauyi.
Sl. 3. Iyakar ɗaukar nauyin ƙasa bisa Terzaghi
Saboda haka, ƙasa a cikin klinin ƙasa ABC, wanda ke tsakanin tushe AB da saman zamewa AC da BC tana ci gaba da kasancewa cikin daidaiton elasticity kuma tana aiki kamar wani ɓangare na tushe. Prism ɗin ABC ba za a iya tura shi ba har sai matsin lamba a gefenta AC da BC sun zama daidai da matsi na ƙasa na gefe na prism ɗin da ke kusa, wato, idan aka wuce iyakar yanayin daidaito, matsin lambar ƙasa mai sakamako q yana aiki a kusurwar ϕ dangane da madaidaiciya ga saman zamewa, wato a tsaye (sl. 3). Tunda a ƙarƙashin tasirin nauyi klinin yana motsi a tsaye ƙasa, matsalar daidaito a cikin ƙasa tana komawa ga tantance matsi na ƙasa mai kaifi. Duk da haka, saboda ƙididdigar ainihin ƙarfin ɗaukar nauyin ƙasa ta wannan hanyar tana da wahala, Terzaghi ya ba da mafita mai sauƙi. Tsarin Terzaghi na ƙididdige ƙarfin ɗaukar nauyin ƙasa na iyaka _q_f ya ce
- Domin ƙafar tushe mai siffar igiya
qf = cNc + γ1 DfNq + 0,5 γ2 BNγ
inda c ke nufin haɗuwar ƙasa
γ1 nauyin ƙasa ta ɗaya a saman ɗafawar tushe
Df zurfin kafa gini daga saman ƙasa zuwa ƙasan tushe
γ2 nauyin kundin ƙasar da ke ƙarƙashin matattarar tushe
B faɗin ƙafar tushe.
Nc, Nq, Nγ su ne abubuwan ɗaukar nauyi, masu dogaro da kusurwar gogayyar cikin ƙasa; ƙimar wannan abin ana ba da ita da waɗannan ƙa’idoji masu zuwa:
Nq wani ƙima ne sakamakon nauyin layin ƙasa na gefe har zuwa zurfin kafuwa: Nq = tg2 (45° + ϕ/2) eπ tg_ϕ_
Nc shi ne ƙimar da ke fitowa sakamakon haɗin kai: Nc = (Nq – 1) ctg_ϕ_
Nγ shi ne faktor ɗin da ke faruwa saboda nauyin kansa na ƙasan yanki ƙarƙashin gindin tushe, wato ƙarƙashin faɗin gindin AB. Brinch Hansen ya ba da shawarar ƙimar wannan faktor a matsayin kusan: Nγ ≈ 1,8 (Nq – 1) tg_ϕ_
Sl. 4. Rarrabar ƙarfafa da ƙasa ke karɓa a lokacin nauyin tsakiyar tsaye na tushe
Saboda ƙaramin bambanci a nauyin girman ƙasa sau da yawa ana ɗaukar γ1= γ2= γ. Bisa ga ma’aunin da ke gaba, ikon ɗaukar nauyi na ƙasa ya dogara (siff. 4) da: haɗuwar ƙasan tushe c, nauyin ƙasa a gefen tushe _γ1 D_F, da nauyin kansa na ƙasar prism ɗin zamewa mai faɗin B.
Sai dai yayin da rabon damuwa da ƙasa ke karɓa saboda tasirin haɗin kai c da zurfin kafuwa Df ya kasance daidai a faɗin dukkanin fadi, wato murabba’i mai kusurwa huɗu, to rabon damuwa da ƙasa ke karɓa saboda tasirin faɗin B yana cikin siffar alwatika, wato mafi girman damuwa ana karɓarsa a tsakiyar tushe, sannan yana raguwa zuwa gefuna inda yake zama sifili.
Sl. 5. Zane-zanen faktor na iya ɗaukar nauyi bisa ga kusurwar gogayyar ciki ta ƙasa a bisa Terzaghi
Ga ƙimomi daban-daban na kusurwa daga 0 zuwa 40°, Terzaghi ya ƙirƙiri jadawalin abubuwan ɗaukar nauyi (sl. 5). Sai dai abubuwan ɗaukar nauyi Nc, Nq da Nγ (layukan cike a hoton 5) za a iya karɓa ne kawai a yanayin ƙasa mai matsewa kuma mai ƙarfi. Idan ƙasa ta yi sako-sako ko tana matuƙar matsewa, to ya kamata a karɓi abubuwan ɗaukar nauyi N’c, N’q da N’γ (layukan yanka a sl. 5), waɗanda ke ba da 2/3 ƙimomin juriyar gogayya. Bugu da ƙari, a wannan yanayin ya kamata a ɗauki 2/3 ƙimomin haɗin kai c da aka samu ta hanyar dakin gwaje-gwaje, ta yadda a wannan yanayin muke da qf = 2/3 cN’c + γ1 DfN’q + 0,5 γ2 BN’γ.
2. Don tushen kafawa mai siffar murabba’i
qf = 2/3 (1+0,3 B/L) cN’c + γ1 DfN’q + 0,5 γ2 BN’γ inda L shi ne tsayin takalmin tushe
3. Don tushen ƙasa mai siffar murabba’i
qf = 2/3 1,3 cN’c + γ1 DfN’q + 0,4 γ2 BN’γ
4. Don ginshiƙin tushe mai siffar zagaye
qf = 2/3 1,3 cN’c + γ1 DfN’q + 0,6 γ2 rN’γ inda r shi ne radius ɗin takalmin tushe.
Don lissafin nauyin ƙasa da aka yarda a ɗauka, ana amfani da abin tsaro F: qa = qf/F. Ƙimar abin tsaro tana tsakanin 2 zuwa 3 gwargwadon yanayin ƙasa da nauyi.
Aikace-aikacen tsarin lissafi
Aiwatar da tsarin lissafi domin ƙayyade nauyin ƙasa da aka yarda da shi yana buƙatar sanin siffofin geomechanics na ƙasa, wato haɗewa da gogayyar cikin ƙasa a zurfin da za a kafa ginin da kuma nauyin kundin ƙasar da ke sama da ƙasa da ƙasan matattarar tushe. Idan ƙasar tushe tana ƙasa da matakin ruwan ƙasa, sai a kuma yi la’akari da ƙarar tashi yayin ƙayyade nauyin kundin ƙasa.
A wajen manyan nauyin ƙasa da manyan gine-gine, idan ana amfani gaba ɗaya da ƙimar nauyin ƙasa da aka yarda da ita da aka samu bisa ka’idojin lissafi, ya kamata a haɗa lissafin ƙarfin ɗaukar ƙasa da lissafin zaman ƙasa. Ana amincewa da ƙarfin ɗaukar ƙasa da aka ƙididdige ne kawai idan lissafin zaman ƙasa ya nuna ƙasa da iyakar da aka yarda da ita ga irin wannan gini. Idan lissafi ya nuna cewa zaman ƙasa ya fi abin da aka yarda da shi, to ƙimar nauyin ƙasa da aka ƙididdige ta hanyar ƙa’idojin lissafi ba za a amince da ita ba, sai a canza hanyar kafuwar gini ta yadda za a samu ƙaramin zaman ƙasa, a cikin iyakar zaman da aka yarda da ita ga irin tsarin ginin.
Fig. 6. Zurfin kafawa mai tasiri D__f
A cikin ƙa’idodin lissafi na tantance iyakar ƙarfin ɗaukar nauyin ƙasa, ba a yi la’akari da gogewar ɓangaren gefen tushe ba, wadda ita ma tana taka rawa a matsayin ƙin jurewa ga tasirin nauyi, idan tushe yana taɓa ƙasa da ƙarfi a bangarorin gefe. Bai kamata a ɗauki ƙarfin gogewar ɓangaren gefen a matsayin abu mai muhimmanci ba, domin a zahiri wannan gogewa tana kasancewa ne kawai a wurin ginshiƙai da ake bugawa cikin ƙasa, yayin da a sawar tushe wannan gogewa kaɗan ce, tunda ana yin sawar ne a cikin ramukan da aka haƙa tun da farko.
Aiwatar da ƙa’idodin lissafi da ba sa la’akari da siffar tushe yana ba da kusan sakamako mafi dacewa ga tushen nau’in layi, wato lokacin da tsawon tushe ya fi faɗinsa sau biyu. Gwaje-gwaje sun nuna cewa a wajen ginshikan tushe masu siffar murabba’i ko da’ira, karyewa yana faruwa a nauyin iyaka wanda ya fi wanda aka ƙididdige da ƙa’idodin lissafi da 10-30%. Ginshikan tushe masu siffar alwatika suna ba da ƙarancin ƙarfin ɗaukar nauyi fiye da na layi, kuma mafi ƙarancin ƙarfin ɗaukar nauyi su ne ginshikan tushe masu siffar zobe idan ba a cike su ba.
Zurfin kafawa Df ana ƙirgawa a matsayin zurfin kafawa mai aiki daga ƙasan kafuwar tushe har zuwa ƙasan tushe (Fig. 6). A cikin kafuwar da ke ƙarƙashin ɗakunan ƙasa, zurfin kafawa mai aiki Df ya bambanta da zurfin kafawa a ƙasa da saman ƙasa. A irin waɗannan lokuta, wajen ƙididdige iyakar nauyi da kuma nauyin ƙasa da aka yarda da shi, ya kamata a koyaushe a ɗauki Df, domin a saman kafuwar tushe akwai iska wadda ba ta tsayayya da tura ƙasa zuwa gefe ƙarƙashin tasirin nauyin kafuwa P.