A yau, Savo Kusić yana mai da hankali kan gilashin katako, itace-aluminum Taga, Taga na al’ada, kofa da buƙatun magana. Wannan rubutun ya kasance azaman ma’ajin ilimin lissafi kuma ba tayin don tsara bangon riƙon ba, binciken kimiyyar ƙasa ko aikin ƙasa.
Hanyoyi na tantance matsa lamba na duniya
Matsin ƙasa mai wucewa yana bayyana ne kawai a cikin yanayin lokacin da nakasar bangon zuwa ƙasa ya isa ya isa don kunna juriya na ciki na ƙasa, wanda ke adawa da ƙarfin waje. Franzius ya kafa ta hanyar gwaje-gwajen da cewa don kunna matsa lamba na duniya, dole ne a motsa bango a yanayin yashi mai yashi s=30_h_1,5, kuma a cikin yanayin yashi karkashin ruwa s_=23h2,5inda ƙaura s ke cikin mm, kuma h shine tsayin bango a cikin m. Saboda haka, idan tsayin bangon shine h=3,0 m, Domin kunna matsa lamba mai wucewa, a cikin yanayin yashi mai yashi, ya zama dole don matsar da bangon zuwa hanyar ƙasa s=156 mm. Duk da haka, tun da irin wannan babban motsi na bango ba a yarda da shi ba a mafi yawan lokuta, ana sarrafa shi ta ɗayan hanyoyi masu zuwa:
a) Idan tsayin bangon ƙanƙanta ne, kamar yadda ya kasance yanayin ƙimar tushe CD (fig.1a), ba’a la’akari da matsananciyar ƙasa mai mahimmanci Ep, idan dai Layer na ƙasa, a gaban ƙafar CD za a iya hako shi ko kuma ya rushe, kuma ana ƙididdige shi kawai tare da matsi na ƙasa mai aiki Ea akan dukkan tsayin bangon AB.
b) A cikin yanayin tsayin bango mafi girma (Fig.1b), maimakon matsananciyar ƙasa mai ƙarfi Ep a ɓangaren bangon CD, Ea ana ɗaukarsa azaman juriya da ke adawa da sojojin Ea1 da Iya2.
c) Game da struts waɗanda ke buƙatar karɓar manyan runduna a kwance, ana buƙatar cikakken matsa lamba Ep akan duk tsayin bangon AB, don adawa da ƙarfin harin R (fig.1c). A wannan yanayin, ƙasa za ta fara lalacewa ta amfani da jacks na hydraulic, kuma idan ƙasa ta ƙunshi yumbu mai laushi ko makamancin haka wanda ke lalacewa da ƙarfi a ƙarƙashin kaya, ana maye gurbin wannan abu a cikin faɗin da ake buƙata b tare da kayan tsakuwa, wanda kusurwar juzu’in ciki yana da girma kuma ana iya haɗa shi cikin sauƙi, ta yadda daga baya nakasar ƙasa ƙarƙashin nauyin tsarin ba a cire ba.
Sl.1. Al’amurran da suka shafi tasirin matsi na ƙasa mai ƙarfi
Akwai hanyoyi da yawa na ƙayyadadden matsa lamba na duniya, daga cikinsu mafi sanannun su ne hanyoyin hoto na Coulomb da Rebhann-Poncelet.
Hanyar zane na Coulomb
Dangane da wannan hanyar, ana ɗaukar saman zamiya na gaske, da kuma juriya na cikin ƙasa ya ƙunshi kawai juzu’i, ba tare da haɗin kai ba (c= =0). Tun da matsi na ƙasa mai ƙarfi ya bayyana azaman ƙarfin juriya, waɗannan sune kusurwar juzu’in ƙasa da kusurwar karkatar da ƙarfi Ep daga al’ada zuwa bangon alamar kishiyar, i.e. -δ da -ϕ (fig.2a).
Idan bangon ciki na bangon AB ne kuma idan muka yi amfani da shimfidar zamiya na sabani AC, karfin waje Ep yana adawa da nauyin W na zamiya ABCA da juriya Q tare da zamiya saman AC. Tun da nauyin W an san shi da girma, shugabanci da shugabanci, yayin da aka san sojojin Q da Ep ta hanyar shugabanci da shugabanci, yana yiwuwa a ƙirƙiri shirin sojojin (Fig.2b), daga inda aka ƙayyade girman ƙarfin Ep.
Sl.2. Coulomb Passive Earth Matsi
Koyaya, tunda ana buƙatar mafi ƙarancin matsa lamba Ep,min, wanda yayi daidai da mahimmancin zamewar saman AC, wanda tare da prism mai zamiya zai yuwu ya zama kuma za’a fitar dashi mafi girma a ƙarƙashin rinjayar ƙarfin waje, ana yin shi kamar haka (fig.3).
Sl.3. Ƙaddamar da matsa lamba na ƙasa EP ta Coulomb
Ana zana filaye da yawa na zamiya AC1, AC2, AC3. . . kuma ga kowane madaidaicin priism na zamiya yana ƙayyade nauyin W1= _AΔABC1_x ku1,00x γ, W2= _AΔABC2_x ku1,00x γ, W3 = AΔABC3 x1,00x γ. Sa’an nan, ga kowane prism, an ƙirƙiri tsarin da ya dace na runduna kuma an ƙayyade dakarun EP1, EP2. Rashin lahani na wannan hanyar shine, saboda maganinta na hoto, yana iya ba da karfi Ep wanda ya kauce wa gaskiya da yawa. Saboda haka, wannan hanya da wuya amfani.
Hanyar hoto ta Culmann
Dangane da wannan hanya, an ɗauka cewa matsa lamba ƙasa mai ƙarfi Ep yana aiki a kusurwa -δ tare da al’ada zuwa bangon tallafi, cewa layin gangaren ƙasa na ƙasa ta mamaye kusurwar -ϕ tare da kwance, kuma cewa layin matsayi ya mamaye kwana (δ+ϕ) tare da layin bango (Fig.4a). A cikin yanayin ƙayyadaddun ma’auni rundunonin aiki guda uku W, Q da Ep sun haɗu a wuri ɗaya. Tun da an san ƙarfin W ta hanya, girma da alkibla, kuma sojojin Q da Ep ta hanya da alkibla, za mu iya zana shirin runduna (fig.4b). Idan muka juya wannan triangle na dakarun kewaye90° - ϕ a cikin madaidaiciyar agogon agogo, ƙarfin W zai faɗi cikin layin layin gangaren ƙasa na ƙasa AN, ƙarfin Q a cikin hanyar zamiya AC, da ƙarfin Ea a cikin layin matsayi BH, tunda tsakanin sojojin W akwai kwana tsakanin ϕ _Q_a tsakanin ϕ Ep kuma na al’ada zuwa bangon akwai kusurwa δ, don haka jagorancin ƙarfin Ep yayi daidai da jagorancin layin matsayi BH (fig.4a).
Sl.4. Ƙaddamar da matsa lamba na ƙasa ta Coulomb
Hanya don ƙayyade matsi na ƙasa mai wucewa shine kamar haka (Fig. 4c). Daga kafar bangon A mun zana sama da dama na zamiya AC1, AC2, AC3….. Kowanne daga cikin waɗannan saman ya yi daidai da priism mai zamewa ABC1, ABC2, ABC3…, wanda tsayinsa daidai da daftarin da muke ɗauka daidai yake da haɗin kai. Idan ma’auni na waɗannan prisms na ƙasa W1= _AΔABC1_x ku1,00x γ, W2= _AΔABC2_x ku1,00x γ, W3= AΔABC3_x ku1,00x γ, inda γ shine ma’aunin nauyi na ƙasa, wanda aka yi amfani da shi zuwa layin gangaren ƙasa na ƙasa AN, za mu sami maki I, II, III1, R2, R3… Triangles A_I_R1, A_II_R2, A_III_R3 su ne jiragen karfi W, Q da Ep don madaidaitan saman zamiya. Ta hanyar haɗa maki R1, R2, R3… mun sami layin Cullmann na matsi na duniya, abin da ake kira Cullmann’s Ep Line. Tangent ga wannan layin daidai da layin gangaren ƙasa yana ba da mafi ƙarancin tsayin KK’, wanda gwargwadon ƙarfin W yana ba da matsi na ƙasa Ep.
Idan muka mika alkiblar AK zuwa mahadar tare da layin kasa, zamu sami madaidaicin madaidaicin juriya AC.
Hanyar Rebhann-Poncelet
Bisa ga wannan hanya, hanya tana kama da wanda aka ƙayyade ma’auni mai aiki na duniya tare da bambanci cewa ƙarfin Q yana aiki a kusurwa - ϕ tare da al’ada zuwa shimfidar wuri, da kuma karfi Ep a kusurwa -δ tare da al’ada zuwa layin bango. A cewar Rebhann, AΔABC = AΔACD (fig.5a). Hanyar tantance matsi na duniya mai wucewa shine kamar haka:
Sl.5. Ƙaddamar da matsa lamba na ƙasa bisa ga Rebhann-Poncelet
Daga ƙafar bangon A muna zana layin gangaren ƙasa a wani kusurwa -ϕ tare da kwance.
Daga saman bangon B muna zana layin matsayi BH a kusurwa (δ+ϕ). A wurin M na mahaɗin matsayi da gangaren yanayin layin ƙasa, ana ɗaga al’ada zuwa mahadar L tare da semicircle sama da AN a matsayin diamita.
Tare da buɗe kompas AL, muna canja wurin batu L zuwa D (AL=AD).
Ta hanyar zana daga aya D daidai da layin matsayi zuwa tsakar C tare da layin ƙasa, muna samun gefe ɗaya na triangle matsa lamba na ƙasa DC = e. Canja wurin batu C zuwa F (DC= DF) da kuma rage CK na al’ada zuwa layin gangaren yanayi na kasa, muna samun triangle na duniya DCF, daga inda muka sami Ep=1/2_γ_ ef, inda γ shine babban yawan ƙasa.
Layin AC yana wakiltar saman zamiya. Zane-zanen matsa lamba na ƙasa shine ba (Fig.5b). Ana samun ta bisa tsari
Ep = xh/2, daga ina x =2_Ep_/h
Wurin kai hari na ƙarfi Ep yana a tsayin tsakiyar nauyi na triangle abc. Ƙarfin Ep yana aiki a kusurwa \ -δ tare da daidaitaccen bangon riƙo.
Hanyoyin da aka bayyana, raka’a, ƙididdiga da ƙididdiga ana canja su daga tushen tarihi kuma ba su maye gurbin nazarin ilimin kimiyyar lissafi ba, ƙididdiga na tsaye, aikin bango ko tsarin aiwatarwa. Yiwuwar haɗakar da juriya mai wuce gona da iri ya dogara da ƙayyadaddun da aka halatta, ainihin sigogi da shimfida ƙasa, ruwa na ƙasa da ƙasa, magudanar ruwa, ƙarin lodi, tasirin girgizar ƙasa, yashwar ƙasa, tonowa, matakan gini da gine-ginen makwabta. Dole ne a ƙayyade mafita ga takamaiman ƙasa ta hanyar bincike mai dacewa da ƙwararrun ƙwararrun geotechnical da masu izini bisa ga ƙa’idodin yanzu.