** Abubuwan da ke cikin ƙwararrun ma’ajiyar kayan tarihi:** rubutu da ƙididdiga na ƙididdiga suna adana lissafin ka’idar tarihi, amma ba binciken ilimin geotechnical ba, aikin bango mai riƙewa, lissafin kwanciyar hankali, kimanta bangon data kasance, shirin tono ko umarnin aiwatarwa. Matsalolin duniya da ruwa sun dogara da ƙayyadaddun ƙasa, rarrabuwa, ƙaddamarwa, magudanar ruwa, ruwan ƙasa, lissafi, motsin bango, ƙarin lodi, sanyi da aikin girgizar ƙasa. Ga kowane lamari na ainihi, ana buƙatar aikin bincike, bayanan dakin gwaje-gwaje, ingantattun ma’auni da tabbatar da haɗin gwiwa ta ƙwararren injiniyan geotechnical da tsarin aiki.

A yau, Savo Kusić yana mai da hankali kan gilashin katako, itace-aluminum Taga, Taga na al’ada, kofa da buƙatun magana. Wannan labarin ya kasance tarihin tarihi kuma baya wakiltar tayin ƙirar ƙirar ƙasa, lissafi ko ginin bangon riƙo.

Matsi na duniya akan bangon riƙewa

Ƙasar da ke da goyan bayan bangon riƙon yana matsa lamba a kanta, yana ƙoƙarin tura ta gaba da fassara (Fig.1a) ko kuma don yin ta’aziyya (Fig.1b). Girman matsa lamba na ƙasa E ya dogara da dalilai da yawa, daga cikinsu akwai mahimman abubuwan da ke cikin ƙasa, nakasar bango, danshi na ƙasa da yanayin ruwa na ƙasa, tsayin bangon, nauyin waje da roughness na ciki na bango.

Tsarin ƙaurawar fassara da jujjuya bangon riƙewa ƙarƙashin aikin matsin ƙasa

Hoto1- motsin fassara da jujjuyawar bango mai goyan baya.

Matsin duniya yana hutawa

Idan bangon riƙon yana da ƙarfi kuma maras motsi, matsa lamba da ke aiki akan shi ana kiransa matsin ƙasa a hutawa kuma ana nuna shi ta E0. Wannan shi ne daidai matsi da ke faruwa a cikin ƙasa mara hankali a zurfin da aka gani, ƙarƙashin rinjayar nauyin ƙasar da kuma yuwuwar ƙaddamar da yadudduka da suka lalace a baya. Matsin ƙasa a hutawa yana da wuya kuma yana faruwa ne kawai a wasu lokuta, kamar tare da bangon riƙewa da aka kafa a cikin dutse mai ƙarfi, sannan tare da rufaffiyar bayanan martaba na tunnels da bututu, tare da manyan docks, waɗanda ba su da motsi gaba ɗaya (Fig.2).

Tsarin matsa lamba na ƙasa a hutawa a gefen bangon babban tashar jirgin ruwa

Hoto2- hutawa matsa lamba na ƙasa akan babban tashar jirgin ruwa.

Matsin duniya mai aiki

Idan bango mai goyan baya ƙarƙashin aikin matsa lamba E yana motsawa gaba ko yana jujjuya madaidaicin ƙafar A, ko wasu ƙananan ma’ana, waɗanda lokuta ne na yau da kullun a cikin ƙasa mai matsawa, ban da rufaffiyar da aka ambata da kuma manyan sifofi, to, ƙasan da ke bayan bangon ta faɗaɗa. Idan motsin bangon yana da girma sosai, wani ɓangaren ƙasa a bayan bangon, prism ABCA, ya karye kuma ya zame saman saman da ke zamewa AC (fig.2). Matsin da prism mai zamewa ke yi akan bangon riƙon ana kiransa matsin ƙasa mai aiki kuma Ea ke nuna shi. Wannan matsa lamba yana da ƙasa sosai fiye da matsa lamba a hutawa, kimanin0,5ku0,7_E0_. Saboda zamewar ƙasa prism ABCA, ƙarfin ƙarfi τ ana kunna shi tare da kafaffen saman zamiya AC, wanda ke adawa da zamewar kuma yana rage matsi na ƙasa. A daidai lokacin da prism ABCA ya fara zamewa, shear stresss τ ya kai ga mafi girman darajarsu, wanda ke nufin cewa a lokacin darajar matsi na duniya mai aiki E shine mafi ƙanƙanta. Saboda haka, Ea shine ƙananan ƙimar ƙimar ƙasa.

Gwajin Terzaghi na matsa lamba na ƙasa tare da kayan yashi akan bango mai tsayi h=1,50 mya nuna cewa don isa ƙananan ƙimar ƙimar matsi na ƙasa mai aiki Ea, ma’anar ƙaurawar bangon Δl na5/10.000tsayin bango ko jujjuya saman bangon Δl na1/5.000_h_ kusa da kafa A.

Matsin ƙasa mai wucewa

Idan muka matsa lamba akan bango daga waje zuwa cikin ƙasa (fig.3), bangon zai koma baya kuma ƙasa za ta ɗaure. Lokacin da motsi na bango ya kai wani ƙimar Δl, prism na ƙasa ABCA zai rabu da ƙasa, wanda za’a tura sama ta wurin zamewa AC ƙarƙashin ƙarin aikin ƙarfin waje. Juriyar da ƙasa ke bayarwa akan aikin ƙarfin waje a lokacin rabuwar prism ABCA shine motsi na ƙasa Ep. Ita ce mafi girman ƙimar iyaka wanda matsatsin ƙasa zai iya kaiwa.

Ana ƙayyade matsa lamba na ƙasa a hutawa ta gwaji, yayin da za a iya ƙayyade matsa lamba na ƙasa mai aiki da ƙididdiga ta hanyar lissafi, ta amfani da hanyoyin nazari ko na hoto, dangane da sanin yanayin jiki na ƙasa, yawanci ƙaddara ta hanyar dakin gwaje-gwaje.

Tsarin matsa lamba na ƙasa da ɗagawa na zamiya priism a bayan bangon riƙewa

Hoto3- matsa lamba na duniya da kuma zamewa prism.

Mahimmanci don aiwatarwa: jihohi masu aiki, m, da marasa aiki ba a zaɓi su ta hanyar ginawa kawai. Ƙunƙarar bangon da aka yarda da ita, damuwa mai tasiri, yanayi mai lalacewa ko rashin ruwa, matakin ruwa na ƙasa da canji, ƙarin kaya da yuwuwar asarar ƙasa a gaban bango dole ne a nuna. Zaɓin da ba daidai ba na yanayin matsa lamba zai iya ɓata kwanciyar hankali na zamewa, jujjuyawa, ƙarfin ɗaukar ƙasa da ƙarfin bango.

Ƙaddamar da ƙayyadaddun matsi na hutawa K0

A cikin yanayin lokacin da bango mai goyan baya ya fallasa tasirin matsa lamba, yakamata a ɗauki matsa lamba E don girman bangon tallafi.0, wanda ya fi matsi na duniya girma. Girman sa yana tsakanin matsa lamba na duniya mai aiki da m, ya danganta da nau’in ƙasa da ƙanƙarar ta.

A zurfin t ƙasa ƙasa, matsi na tsaye saboda nauyin ƙasa shine σt = γ·t. Idan babu yiwuwar fadada ƙasa ta gefe, matsa lamba a kwance σh = γ·t·_K yana aiki a zurfin _t_0,_ku K0 = σh/σt.

K0shine matsi na hutawa. Za’a iya ƙayyade ƙimar ƙarfin hutawa ta gwajin triaxial kamar haka.

Ana sanya samfurin ƙasa mara kyau da aka ɗauka daga zurfin matsi na hutawa a cikin na’urar triaxial, inda matsa lamba na gefe σ3_Lokacin da ake saka kaya a tsaye σ1 yana daidaitawa don kada nakasar gefe ta faru, watau nakasar gefen samfurin daidai yake da sifili. Ma’auni na ingantaccen ƙarfin lantarki da aka samu ta wannan hanyar σ’1 da σ’3_An tsara su akan zanen σ’1- σ’3(fig.4), kuma ana samun tangent madaidaiciya zuwa sashin farko na zane, gangaren wanda ke ƙayyade ƙimar K.0 = σ’3/ σ’1.

Hoto na ingantattun abubuwan da suka fi dacewa don tantance ƙimar hutu ta gwajin triaxial

Hoto4- ƙayyadaddun ƙididdiga K__0matsa lamba ta hanyar gwajin triaxial.

A cewar Petermann, ma’aunin ma’aunin matsi na hutu shine

don dunƙule yashi            K0 =0,40-0,45

don sako-sako da yashi       K0 =0,45-0,50

don yumbu                            K0 =0,60-0,75

Kimar dakin gwaje-gwaje: Kimanin jeri da ke ƙasa sun kasance ɓangare na ainihin rubutun, amma ba madadin gwajin samfurin wakilci ba, ƙirar ƙasa da ƙima ƙira. Dole ne a bincika bayanin OCR na ƙididdiga, rubuto-rubutu da ridda akan wata madaidaicin tushe kafin kowane lissafi.

Hanyoyi na tantance matsa lamba na duniya - Ka’idar Coulomb

Coulomb ya fara buga ka’idar matsin duniya (1770. shekara), dangane da kwarewar filin. Ya kalli bangon da ke riƙe da ƙasa maras kyau. A wani lokaci ya cire bangon, ta yadda girman duniya ya zame wani wuri mai zamewa AC, ya karkata a kusurwa a tare da kwance (fig.5). Nauyin W na zamiya prism duniya ABC, mai iyaka da filin ƙasa BC, da sliding surface AC da bangon riƙewa AB, yana aiki lokaci guda akan bangon riƙon da saman zamiya. Coulomb ya ƙaddara girman matsi na duniya mai aiki Ea ƙarƙashin zato guda biyu masu zuwa:

  1. cewa farfajiyar zamiya ita ce ainihin farfajiya;

  2. cewa rundunonin aiki guda uku: nauyin prism mai zamiya W, juriya na bango mai goyan baya Ea da juriyar juriya Q tare da zamewar saman AC suna haɗuwa a wuri ɗaya, wanda ke nufin cewa an rufe jirgin na sojojin. Bisa ga wannan zato, a cikin yanayin ƙayyadaddun ma’auni nauyin W an soke shi lokaci guda ta hanyar juriya na bango mai goyan baya Ea da juriya mai juriya Q tare da saman zamewa.

Coulomb’s zamiya prism a bayan bango da shirin sojojin nauyi, gogayya da matsa lamba na duniya

_Hoto5- Ƙaddamar da matsa lamba na duniya bisa ga ka’idar Coulomb.

Zato na baya bai dace da gaskiya ba. Fuskar zamewar ba madaidaiciya ba ce amma shimfida ce mai lankwasa. Ƙaddamarwar rundunonin aiki guda uku kawai tana kasancewa ne kawai a cikin yanayi ɗaya, lokacin da saman filin bayan bango ya kasance a kwance, saman bangon na ciki yana tsaye kuma hanyar karfi Ea a kwance, yayin da babu shi a cikin sauran lokuta. Koyaya, duk da waɗannan ɓangarorin, ƙudurin matsa lamba na duniya har yanzu yana dogara ne akan ka’idar Coulomb, kamar yadda ta tabbatar a zahiri ana iya amfani da ita a lokuta da yawa.

Don ƙayyade matsa lamba na ƙasa mai aiki Ea Coulomb ya ɗauka cewa saboda sakamakon nauyin nauyin nauyin duniya W akwai motsi na bangon goyon baya da kuma samuwar prism ABC na matsa lamba na duniya. Zaton cewa juriya na ciki na ƙasa ya ƙunshi kawai gogayya. Coulomb yana lalata nauyin W zuwa sassa biyu, ɗayan a cikin jagorancin ƙarfin ƙarfin duniya mai aiki Ea, ɗayan a cikin hanyar juriya mai juriya Q tare da saman zamiya (fig.5b). A cikin yin haka, Coulomb ya ƙara ɗauka cewa sashin yana aiki a kusurwar juzu’i na ciki tare da al’ada zuwa saman zamiya AC, kuma ɓangaren Ea yana aiki a kusurwar karkata δ tare da al’ada zuwa saman ciki na bango AB. Ƙarfin W an ƙaddara ta hanya, girma, da alkibla.

Don wani wuri mai zamewa a kusurwa α tare da kwance, ana samun ƙarfin W daga saman prism na ƙasa ABC na tsawon tsayi.1,0 mdaidai gwargwado ga tsari da nauyin ƙasa mai girma γ, W=AΔABC x1,00x γ. An san sojojin Ea da Q ta hanya. Dangane da tsarin sojojin (Fig.5b) da sine theorem da muke da:

Tsarin da aka bincika ta hanyar amfani da sine theorem zuwa jirgin sojojin

Tsarin shari’ar musamman na riƙe bango tare da filin kwance da jirgin sama mai ƙarfi

Hoto6- yanayin tsaka-tsakin sojojin da ke aiki a lokaci guda.

Wannan tsarin yana daidai ne kawai a yanayin lokacin da ƙasa ke kwance (v=0), saman ciki na bango yana tsaye (θ=0) da kuma jagorancin karfi Ea kwance (δ=0) watau lokacin da bangon ya yi santsi (fig.6).

Don wannan musamman abin da ake kira shari’ar Rankine muna da:

Tsarin matsi na duniya mai aiki don shari’ar Rankine na musamman

Nauyin W yana cikin wannan yanayin W =0.5· γ·h_2/tg_α, inda γ shine ma’aunin nauyi na ƙasa.

Idan muka gabatar da ƙimar gaba a cikin ma’auni don Ea, zamu sami:

Tsarin dabarar matsi na duniya mai aiki a matsayin aikin kusurwar saman zamiya

Ma’aunin da ya gabata yana nufin madaidaicin wuri mai zamewa AC. Duk da haka, yana da mahimmanci don ƙayyade ƙarfin Ea don mahimmancin zamiya mai mahimmanci, watau wanda zamewa zai iya faruwa. Zai zama saman da ke ba da ƙimar mafi girman ƙimar matsa lamba na ƙasa max Ea.

Domin tsayin bangon H da aka ɗauka akai-akai na gogayya ta ciki ϕ, ƙimar matsi na ƙasa mai aiki ya bambanta tare da kusurwar karkata α na saman zamiya zuwa kwance. Za a sami ƙimar max Ea idan muka bambanta Ea ta α kuma muka saita bambancin daidai da sifili:

Tsarin lissafin lissafi don tantance mahimmin kusurwa da ƙididdiga na matsa lamba na duniya

Formula ba lissafin lissafi ba ne: ƙididdigar ƙila za ta iya samun baƙaƙen ƙira, fihirisa, kusurwoyi da alamu. Ba a kwafi su cikin aikin ba tare da kwatanta tare da ingantaccen tushen ƙwararru ba, duba raka’a, zato samfuri da sarrafa sakamako mai zaman kansa. Dole ne lissafin ya haɗa da ruwa, magudanar ruwa, lodi tare da kambin bango, aikin girgizar ƙasa da duk iyakokin iyaka masu dacewa.

Ƙaddamar da kusurwa ϕ da δ

An ƙayyade kusurwar gogayya ta ciki ϕ a cikin dakin gwaje-gwaje. Girman sa ya dogara da nau’in ƙasa, zafi da ƙaddamarwa. Ga wasu nau’ikan ƙasa, ƙimar kusurwar ϕ yawanci tana jeri cikin iyakokin da aka bayar a cikin tebur 1.

Table na tarihi na kimanin kusurwoyi na gogayya na ciki don dakataccen dutse, tsakuwa, yashi, loam, loess da yumbu

Table 1 - Kimanin dabi’u na kusurwar gogayya ta ciki ϕ don wasu nau’ikan ƙasa.

A kusurwar karkata δ na karfi Ea daga al’ada zuwa ciki na bango ya dogara da nakasar bango da ƙasa a bayansa da kuma a kan roughness na ciki na bango. Idan sulhu na ƙasa ya fi girma fiye da ginin bango, wanda shine mafi yawan lokuta, to, kusurwar δ yana da kyau, rikici tsakanin bango da ƙasa yana aiki zuwa sama. Idan daidaitawar bangon ya fi girma fiye da daidaitawar ƙasa, wanda shine lamari na musamman, to, kusurwar δ ba ta da kyau, rikici tsakanin bango da ƙasa yana aiki a ƙasa. Ƙayyadaddun ƙimar kusurwa δ don bangon bango gaba ɗaya mai santsi ne δ=0, don madaidaicin gaba ɗaya δ=ϕ. Gabaɗaya, δ=2/3_ϕ_ an karbe shi, tare da gaskiyar cewa ƙasan bangon tana da kariya ta dindindin daga jika mai ƙarfi. Idan ƙasa a bayan bangon ta fallasa ga girgizar ƙasa mai ƙarfi, δ=ϕ/2 ana karɓa, kuma idan ta jika sosai δ=0.

** Ƙimar ƙira ta kusurwa:** ma’auni da ƙididdiga masu mahimmanci ϕ da δ ba su da amfani kai tsaye ga takamaiman wuri. Zaɓin ma’auni dole ne ya dace da nau’in da yanayin ƙasa, hanyar shigarwa da ƙaddamarwa, magudanar ruwa, motsin da ake tsammani na bango, rashin daidaituwa na lamba da tsarin aikin da ya dace.

Rarraba matsi na ƙasa a bayan bango da kuma wurin harin da karfi Ea

Tsarin filaye masu zamewa da rarraba matsa lamba na triangular lokacin da bango ya juya kusa da kafa

Hoto7- rarraba matsa lamba na ƙasa yayin jujjuyawar bangon tallafi a kusa da wurin ƙafa A.

Rarraba matsa lamba na ƙasa tare da bangon ciki na bango ya dogara da lalacewar bangon tallafi, akan siffar ƙasa a bayan bango da kuma siffar bangon ciki.

Wurin kai hari na matsa lamba na ƙasa mai aiki Ea ya dogara da rarraba matsa lamba tare da bangon ciki na bango da kuma siffarsa. Kullum yana kan tsayin tsakiyar nauyi na saman zanen matsa lamba.

Coulomb ya yarda cewa matsa lamba na ƙasa a bayan bangon yana ƙaruwa daidai da zurfin, kamar yadda yake da ruwa, abin da ake kira. hydrostatic rarraba matsa lamba na ƙasa (fig.7). Koyaya, rarraba matsi na hydrostatic yana wanzuwa ne kawai a cikin yanayin lokacin da bangon ke juyawa kusa da ƙafar A ko wani ƙaramin ƙasa, yayin da a duk sauran lokuta ya ɓace daga gare ta.

Idan bangon da ke goyan bayan yana jujjuya madaidaicin ƙafar A, ko wani ƙaramin ma’ana, ƙasa tana motsawa zuwa ƙasa (Fig.7a), inda babu turawa zuwa cikin ƙasa. A wannan yanayin, zamewar ƙasa yana faruwa akan saman mafi ƙarancin juriya M1C1, M2C2… layi daya da zamewar saman AC, wanda ke faruwa lokacin jujjuyawar bangon ya isa ya samar da prism mai zamiya ABCA.

Sabili da haka, a cikin wannan yanayin, matsa lamba yana ƙaruwa daidai da zurfin, watau rarraba matsa lamba na ƙasa bisa ga Coulomb hydrostatic. Za a sami zane mai aiki na duniya dangane da ilimin ƙarfin Ea da tsayin bangon h, tunda ƙarfin Ea daidai yake da yanki na zane-zanen matsa lamba abc (Fig.7b):

Ea=x·h/2, daga ina x=2Iya/h,

wato, tun Ea = ½ γh2Ka, x = γhKa.

Tsarin rarraba matsi mai aiki da rashin ƙarfi lokacin jujjuya bangon kusa da saman ko mafi girma

Hoto8- Rarraba matsa lamba na ƙasa lokacin da bangon ya juya kusa da saman B ko wani matsayi mafi girma L.

Idan bangon da ke goyan bayan ya juya saman bangon B ko wani wuri mafi girma L (fig.8a), akwai turawa a ɓangaren sama zuwa cikin ƙasa, wanda saboda haka ana tura shi sama tare da saman mafi ƙarancin juriya M.1C1, M2C2…

A isasshe babban jujjuyawar bangon, an samar da wani wuri mai zamewa AC, tare da zamewar prism mai zamewa zuwa ƙasa yayin extrusion. Sakamakon tura ƙasa a cikin ɓangaren sama, matsa lamba na ƙasa yana bayyana, wanda ya fi girma fiye da mai aiki, kuma a cikin wannan ɓangaren zanen matsa lamba bd yayi daidai da matsa lamba Ep (fig. 8b). Kamar yadda jimlar matsa lamba na ƙasa Ea ya dogara da girman prism na ƙasa ABCA kuma yana daidai da saman triangular na zanen matsa lamba abe, wannan zanen zai ragu a gaba da gaba, har sai samansa ya zama daidai da saman triangular abe. Ainihin matsi na matsi a wannan yanayin shine curvilinear bc, wanda ba za a iya tantance shi ta hanyar lissafi ba. Duk da haka, tsakiyar nauyi S na saman zanen ac yana sama da tsakiyar tsakiya na farfajiyar zane mai triangular, wanda ba shi da kyau ga kwanciyar hankali na bangon riƙewa, saboda wurin harin da karfi Ea ya fi girma. A cewar Terzaghi, yana kusa da rabin tsayin bangon tallafi.

Idan bangon tallafi yana motsawa gaba a cikin fassarar (fig. 9a), matsin lamba wanda kafin motsi yayi daidai da matsa lamba na ƙasa a cikin yanayin hutawa E0 yana raguwa, ta yadda ba a bayyana saman ƙasan juriya ba, amma lokacin da bangon ya motsa sosai, yayin da AC_A_Prism ke haifar da ƙasa. nunin faifai zuwa ƙasa. Tun da jimlar matsa lamba daidai yake da yankin triangular na zane-zanen matsa lamba abe (fig. 9b), zanen matsa lamba zai ragu a cikin gaba. Ainihin zanen matsi shine layin mai lankwasa ac, wanda ba za’a iya tantance shi ta hanyar lissafi ba. A cewar Terzaghi, tsakiyar nauyi S yana kan tsayi 0,40 - 0,45_h_.

Tsarin rarraba matsi na curvilinear yayin motsi gaba na fassarar bangon riƙewa

Hoto 9 - Rarraba matsa lamba na ƙasa yayin motsi fassarar bangon riƙewa gaba.

Yin la’akari da hanyar ƙayyade matsa lamba na ƙasa a matsayin matsananciyar ƙima, mafi girma ga aiki kuma mafi ƙanƙanta don m, ka’idar Coulomb ana ɗaukarsa a matsayin hanya mai mahimmanci na ƙayyade matsa lamba na duniya.

** Bayanan injiniya na ƙarshe: ** rarrabawa da matsi na harin ya dogara ne akan ainihin hanyar da aka lalata tsarin. Baya ga matsa lamba na ƙasa, magudanar ruwa da matsa lamba na ruwa, kwanciyar hankali na duniya da na ciki, zamewa, ƙaura, ɗaukar ƙasa da daidaitawa, ƙarfin bango da tushe, yashwar ƙasa, leaching, matakan tono da kwanciyar hankali na ɗan lokaci dole ne a duba. Yanayin bangon da ke akwai wanda ke nuna motsi, tsagewa, buguwa ko zubar da ruwa mara sarrafa yana buƙatar kima na ƙwararru nan take.