Kumatshini womhlaba kumiselwa umthamo wokuthwala wokugqibela womhlaba kunye nomthwalo ovumelekileyo womhlaba.
Amandla okuthwala aphezulu omhlaba ngawo afikelelwa ngexesha lokuvela kokuqhekeka komhlaba. Ukuqhekeka komhlaba kwenzeka xa umthwalo apho isiseko sisebenza ngawo emhlabeni udlula amandla ayo okucheba. Kule meko, phantsi kwempembelelo yomthwalo wesiseko P kuvela iindawo zokuxhathisa okuncinci ACD kunye BCE – imiphezulu yokutyibilika kumz. 1, apho umhlaba utyhalelwa ecaleni yaye ngexesha elinye kuvela ukuphakama komhlaba ngaphezu komphezulu womhlaba kufuphi nesakhiwo DG kunye EF, logama isiseko ngokwaso siqala ukutshona.
Sl. 1. Ukuqhekeka komhlaba phantsi kwesenzo somthwalo wesiseko
Amandla okucheba omhlaba ayanda ngokunyuka kobunzulu besiseko t, kuba ngenxa yobunzima bemaleko ephezulu kuncipha amathuba okutyhalwa ecaleni. Ngoko ke, iziseko ezinzulu zidityaniswa kancinci nokophuka komhlaba, ngoxa iziseko ezingekho nzulu zingozi ekwaphukeni. Ngokunjalo, iziseko ezibanzi zidityaniswa kancinci nokophuka komhlaba, kuba imiphezulu yokutyibilika iba nzulu ngakumbi.
Umthwalo ovumelekileyo womhlaba ngulo unokuthi uvunyelwe ukuba usebenze emhlabeni ngendlela yokuba kungabikho kophuka komhlaba phantsi kweemeko ezimbi kakhulu ezinokubakho. Umthwalo ovumelekileyo womhlaba umiselwa ngokusekelwe kumthamo wokuthwala umda womhlaba ngokusebenzisa umba wokhuseleko. Ubukhulu bomba wokhuseleko buxhomekeke kwizinto ezininzi, phakathi kwazo ezona zibalulekileyo kukuchaneka kweempawu zomzimba zomhlaba, amathuba okutshintsha kwamaxabiso ezinto zokuxhathisa zangaphakathi zomhlaba ngakumbi ukudibana, elinokutshintsha kakhulu phantsi kwempembelelo yamanzi emhlabeni, emva koko impembelelo yezinye izinto ezinokubakho, ezifana neemeko zomthwalo (amathuba omthwalo wesiquphe nowamandla), ubunzulu bokusekwa kwesiseko, nobubanzi besiseko.
Umthamo wokuthwala womhlaba unokumiselwa ngokusekelwe ekuqhekekeni komhlaba, okunika umthamo wokugqibela wokuthwala. Ngaphantsi komthamo wokugqibela wokuthwala komhlaba kuqondwa ubungakanani bomthwalo obangela uqhekeko. Kukho iindlela ezimbini zokumisela umthamo wokugqibela wokuthwala ngokusekelwe ekuqhekekeni komhlaba, ezizezi isisombululo semathematika kunye nomthwalo wovavanyo.
Isisombululo semathematika
Oosonzululwazi abaninzi bazamile ukufumana isisombululo semathematika sokumisela umthwalo wokugqibela womhlaba, ngokusekelwe ekwazini izinto ezichaphazela oku nangeengcinga ezahlukeneyo malunga neemeko zokophuka. Izinto ezichaphazela oku ziimpawu zomzimba womhlaba, ezimiselwa ngeemvavanyo zaselebhu kwiisampulu zomhlaba ezingaphazamisekanga, imeko yamanzi angaphantsi komhlaba, ubunzulu besiseko, ubungakanani nokumila komphezulu osetyenziswayo womthwalo, kwakunye nendlela yokulayisha, oko kukuthi, ukulayisha okufanayo okanye okungalinganiyo, okuphakathi okanye okuphambukayo komhlaba. Iingcinga ngeemeko zokophuka zisekelwe kwithiyori yeplastikhi nakwithiyori ye-elasticity. Noko ke, iindlela zangoku zokumisela umthamo wokuthwala womhlaba zisekelwe kwithiyori yeplastikhi, edityaniswe nezinye iingcinga ezenziwe lula.
Apha siza kubonisa iindlela ezimbalwa zokubala ezaziwayo zokumisela umthamo wokuthwala osebenzayo wokugqibela, oko kukuthi umthwalo ovumelekileyo womhlaba.
Ifom yePrandtl-Caquota
Ukuba unyawo lwesiseko AB lumiliswe kubunzulu t ngaphantsi komphezulu womhlaba, kobu bunzulu kubakho uxinzelelo lokunxibelelana po ngenxa yomthwalo wesiseko kunye noxinzelelo olusecaleni p=γt ngenxa yobunzima bomhlaba ongaphezulu ukusuka kwinqanaba lonyawo lwesiseko ukuya kumphezulu womhlaba (sl. 2).
Phantsi kwesenzo esithe ngqo sobunzima besiseko, ngexesha lokugqithisa umda wokuthwala womhlaba kuvela iindawo ezithe tye zokutyibilika AC kunye BC, ezibumba i-engile α = 45° + ϕ/2 kunye nomphezulu othathelwe umthwalo. Ezi ndawo zityibilikayo zenza iprism yomhlaba esebenzayo ABC.
Umz. 2. Imiphezulu yokutyibilika emilo ye-spirali yelogarithm phantsi kwempembelelo yesiseko esinomthwalo osemzantsi ngokwePrandtl-Caquot
Phantsi koxinzelelo lweprizim yomhlaba esebenzayo kubakho ngasemacaleni iiprizim zomhlaba ezingenziyo ADD1 kunye BEE1, ekuzama ukuzityhalela phezulu ngemigangatho yokutyibilika DD1 kunye EE1, nge-engile ye 45°-ϕ/2 kunye ne-horizontal. Phakathi kwendawo yoxinzelelo lomhlaba esebenzayo kunye nengasebenziyo kukho indawo yokucheba kweradial ACD okanye BCE, apho xa kugqitywa umda wokulingana ukutyibilika kwenzeka kwimigangatho egobileyo yokutyibilika. URésal wabala ukuba imiphezulu yokutyibilika kwindawo yokucheba kweradial ikwimo ye-spiral ye-logarithm enepali ku A okanye B, enesibalo r=r0 eπ tg_ϕ_
Ukuze kumiselwe umthwalo womda womhlaba, kuqwalaselwe ezi ngcinga zilandelayo:
- ukuba isiseko sithambile, oko kukuthi, ukukhuhlana phakathi konyawo lwesiseko nomhlaba kuyajongwa njengokungabalulekanga;
- ukuba amandla okushearing omhlaba ecaleni kwemigangatho D1M kunye E1N akakho, oko kukuthi akahoywa;
- uba ubunzima bomthamo womhlaba phantsi kweseko γ=0, oko kukuthi impembelelo yobunzima bomhlaba phantsi kweqaqa lesiseko iyashiywa ingqalelo, kwindawo yolungelelwano lweplastiki.
Ifom yesiPrandtl-Caquota ithi:
Umthamo womda wokuthwala umhlaba ngu
Ukuba sibeka:
umda wokuthwala womhlaba odityanisiweyo ngu qf = γtm + cm1.
Kwimilinganiselo eyahlukeneyo ye-engile yokungqubana kwangaphakathi komhlaba, amaxabiso ka m no m1 anikiwe kwitafile 1.
Tabl. 1. Amaxabiso ee-coefficients m kunye m__1 kwiinqanaba ezahlukeneyo ze-engile yokungqubana kwangaphakathi komhlaba
Umthwalo womhlaba ovumelekileyo ngu qa = pdozv = qf/F apho F ingumlinganiso wokhuseleko. Ngokusetyenziswa kwefomula kaPrandtl-Caquot kwamkelwa F = 4, ngoko ke qa = qf/4.
Ifomula kaTerzaghi
UTerzaghi wanika ifomula ye-semi-empirical yokubala umthamo wokuthwala ongumda womhlaba phantsi kwesenzo semithwalo yemilo yomgca, isikwere kunye nediski ejikelezileyo. Wajonga isiseko esakhiwe kubunzulu Df ngaphantsi komphezulu womhlaba, ngobubanzi B (umz. 3), waza wamkela ukuba kukho ukhuhlano phakathi kweflethi yesiseko AB nomhlaba, oluchasa ukutyhalwa komhlaba ecaleni, nokuba imiphezulu yokutyibilika AB kunye BC yenza i-engile yokhuhlano lwangaphakathi kunye nomphezulu othwalayo.
Sl. 3. Amandla omda omhlaba ngokukaTerzaghi
Ngenxa yoko, umhlaba okwiklinya yomhlaba ABC, obandakanyiweyo phakathi kwesiseko AB kunye nemiphezulu yokutyibilika AC kunye BC uhlala ukwimeko yokulingana okuthambileyo kwaye uziphatha njengenxalenye yesiseko. Iprism ABC ayinako ukutyhalelwa phambili kude kube ngoko, de uxinzelelo kumacala ayo AC kunye BC lube lulingana noxinzelelo lomhlaba olusebenzayo lweeprism ezisecaleni, nto leyo ethetha ukuba, xa kugqityiwe imeko yomda wokulingana, uxinzelelo lomhlaba oluphuma ku q lusebenza nge-engile ϕ ngokunxulumene ne-normal kumphezulu wokutyibilika, oko kukuthi kwicala elithe nkqo (umz. 3). Kuba phantsi kwesenzo somthwalo iklinya ihamba iye ezantsi ngokuthe nkqo, ke ingxaki yokulingana emhlabeni iba kukuqinisekisa uxinzelelo lomhlaba olusebenzayo. Nangona kunjalo, ngenxa yokuba ukubalwa ngokuchanekileyo komthamo wokuthwala womhlaba ngale ndlela kunzima, uTerzaghi wanika isisombululo esenziwe lula. Ifomula kaTerzaghi yokubala umthamo womhlaba wokuthwala umda _q_f ithi
- Kwisiseko esenziwe ngendlela yebhanti
qf = cNc + γ1 DfNq + 0,5 γ2 BNγ
apho c kukudibana komhlaba
γ1 ubunzima bomthamo womhlaba ongaphezulu kwesiseko sesiseko
Df ubunzulu bokusekwa ngaphantsi komphezulu womhlaba ukuya ezantsi kwesiseko
γ2 ubunzima bomhlaba ngomthamo ongaphantsi kweziseko
B ububanzi besiseko sesemente.
Nc, Nq, Nγ zizinto zokuthwala umthwalo, ezixhomekeke kwikona yokukhuhlana kwangaphakathi komhlaba izinto zolu phawu zinikwe ngale mizekelo ilandelayo:
Nq yinto ephuma kubunzima bomaleko osecaleni womhlaba ukuya kubunzulu besiseko: Nq = tg2 (45° + ϕ/2) eπ tg_ϕ_
Nc yinto ebangelwa kukuhlangana: Nc = (Nq – 1) ctg_ϕ_
Nγ yinto ebangelwa bubunzima bayo bodwa becandelo lomhlaba eliphantsi kwesihlalo sesiseko, oko kukuthi phantsi kobubanzi besihlalo AB. Ixabiso lale nto uBrinch Hansen uliphakamisa njengelisondeleyo: Nγ ≈ 1,8 (Nq – 1) tg_ϕ_
Sl. 4. Ukwabiwa koxinzelelo olufunyanwa ngumhlaba phantsi komthwalo othe nkqo ongundoqo wesiseko
Ngenxa yomahluko omncinane wobunzima bomhlaba ngomthamo, kudla ngokwamkelwa γ1= γ2= γ. Ngokwe-equation engentla, umthamo wokuthwala womhlaba uxhomekeke (fig. 4) kwezi: ukudityaniswa komhlaba osisiseko c, umthwalo womhlaba ecaleni kwesiseko _γ1 D_F, ubunzima bomhlaba obuzimeleyo beprizim eshiyekileyo esityibilikayo enobubanzi B.
Nangona kunjalo, ngoxa ulwabiwo lweengcinezelo olwamkelwa ngumhlaba ngenxa yefuthe le-cohesion c nobunzulu bokusekwa Df lulinganayo kububanzi bonke, oko kukuthi luyoxande, ulwabiwo lweengcinezelo olwamkelwa ngumhlaba ngenxa yefuthe lobubanzi B luyonxantathu, oko kukuthi iingcinezelo ezinkulu zamkelwa embindini wesiseko, zize zehle zisiya emacaleni apho zilingana no-zero.
Umz. 5. Idayagram yomlinganiso womthamo wokuthwala ngokuxhomekeke kwi-engile yokhuhlano lwangaphakathi lomhlaba ngokukaTerzaghi
Kumaxabiso ahlukeneyo ekona ukusuka ku 0 ukuya ku 40°, uTerzaghi wayila iidayagram zobuchule bokuthwala umthwalo (sl. 5). Nangona kunjalo, izinto zobuchule bokuthwala umthwalo Nc, Nq kunye Nγ (imigca eqhubekayo kumfanekiso 5) zinokwamkelwa kuphela kwimeko yomhlaba odityanisiweyo nowomeleleyo. Ukuba umhlaba ukhululekile okanye ucinezeleka ngakumbi, ngoko kufuneka kwamkelwe izinto zobuchule bokuthwala umthwalo N’c, N’q kunye N’γ (imigca eqhawukileyo kwisl. 5), ezinikela 2/3 amaxabiso oxhathiso lokungqubana. Ukongeza, kule meko kufuneka kuthathwe 2/3 amaxabiso okudityaniswa c afunyenwe ngelebhu, ukuze kule meko sibe no qf = 2/3 cN’c + γ1 DfN’q + 0,5 γ2 BN’γ.
2. Kwisiseko esingunxande
qf = 2/3 (1+0,3 B/L) cN’c + γ1 DfN’q + 0,5 γ2 BN’γ apho L bubude besiseko esihlala emhlabeni
3. Kwisiseko somhlaba esinomumo wesikwere
qf = 2/3 1,3 cN’c + γ1 DfN’q + 0,4 γ2 BN’γ
4. Kwisiseko esiyingqukuva
qf = 2/3 1,3 cN’c + γ1 DfN’q + 0,6 γ2 rN’γ apho r iliradiyasi yesiseko sesithende.
Ekubalweni komthwalo ovumelekileyo womhlaba kuthathwa into yokhuseleko F: qa = qf/F. Ixabiso le-factor yokhuseleko lisukela ku 2 ukuya ku 3 ngokweemeko zomhlaba nomthwalo.
Ukusetyenziswa kweepateni zemathematika
Ukusetyenziswa kweendlela zezibalo zokumisela umthwalo ovumelekileyo womhlaba kufuna ulwazi ngeempawu ze-geomechanical zomhlaba, oko kukuthi ukudibana nokukhuhlana kwangaphakathi kubunzulu besiseko kunye nobunzima bomthamo womhlaba ongaphezulu nangaphantsi kwesiseko. Ukuba umhlaba wesiseko ukwindawo engaphantsi komgangatho wamanzi aphantsi komhlaba, kufuneka kuthathelwe ingqalelo nokunyuswa xa kumiselwa ubunzima bomthamo womhlaba.
Xa kukho imithwalo emikhulu yomhlaba nezakhiwo ezikhulu, xa ixabiso elifunyenweyo lomthwalo ovumelekileyo womhlaba ngokusekelwe kwiindlela zemathematika lisetyenziswa ngokupheleleyo, ukubalwa komthamo wokuthwala umhlaba kufuneka kuhambisane nokubalwa kokuhlala phantsi. Umthamo wokuthwala obalwayo womhlaba wamkelwa kuphela xa ukubalwa kokuhlala phantsi kuvelise ukuhlala okuncinci kunoko kuvumelekileyo kudidi oluthile lwesakhiwo. Kwimeko apho ukubalwa kuvelise ukuhlala okukhulu kunoko kuvumelekileyo, ixabiso elibalwayo lomthwalo ovumelekileyo womhlaba ngokusebenzisa iindlela zokubala alwamkelwa, koko kufuneka kutshintshwe indlela yokuseka isiseko ukuze kufumaneke ukuhlala okuncinci, ngaphakathi kwemida yokuhlala okuvumelekileyo kwisakhiwo esithile.
Sl. 6. Ubunzulu obusebenzayo besiseko D__f
Kwiifomula zemathematika zokumisela umthamo osesiphelweni wokuthwala womhlaba, ukungqubana komkhono wesiseko akuzange kuthathelwe ingqalelo, nangona nako kuthatha inxaxheba njengokuxhathisa ngokuchasene nesiphumo somthwalo, ukuba isiseko sidibana ngokuqinileyo nomhlaba emacaleni. Ukuxhathisa ngokungqubana komkhono akufanele kuthathelwe ingqalelo, kuba ukungqubana kwangempela komkhono kubakho kuphela kwiipali eziqhutyelwa emhlabeni, ngelixa kwiziseko zomqamelo ukungqubana komkhono kuncinci, kuba imiqamelo yenziwa kwimigodi embiweyo kwangaphambili.
Ukusetyenziswa kweefomula zemathematika apho kungathathelwa ngqalelo imilo yesiseko kunika iziphumo ezisondeleyo kakhulu kwiziseko ezimile njengebhanti, oko kukuthi xa ubude besiseko bungaphezu kokuphinda kabini ububanzi baso. Iimvavanyo zibonise ukuba kwiziseko ezimile isikwere okanye isetyhula, ukwaphuka kwenzeka kumthwalo womda ongaphezulu ngo 10-30% kunoko kubaliweyo ngeefomula zemathematika. Iziseko ezimile unxantathu zinika amandla athwalayo amancinci kunebhanti, yaye awona mandla athwalayo amancinci anikwa ziziseko ezimile iringi, ukuba azizaliswanga.
Ubunzulu bokusekwa Df bubalwa njengobunzulu bokusekwa obusebenzayo ukusuka phantsi komhlaba wesiseko ukuya ezantsi kwesiseko (Sl. 6). Kwiisiseko ezingaphantsi kweendawo ezingaphantsi komhlaba, ubunzulu bokusekwa obusebenzayo Df buyahluka kubunzulu bokusekwa naphantsi komgangatho womhlaba. Kwiimeko ezinjalo, ekubaleni umda womthwalo kunye nomthwalo ovumelekileyo womhlaba kufuneka kuhlale kwamkelwa Df, kuba ngaphezulu komhlaba wesiseko kukho umoya ongachasi ukutyhalelwa ecaleni komhlaba phantsi kwempembelelo yomthwalo wesiseko P.