A ƙarƙashin nauyi, kowace ƙasa, sai dai dutsen ƙarfi, tana zama ƙasa. Zama ƙasa gaba ɗaya yana faruwa ne daga dalilai biyu: matsewar ƙasa wato rage girman ta sakamakon fitar da iska ko ruwa daga cikin ramukanta da kuma turawar ƙasa ta gefe kusa da gefunan tushe sakamakon zamewar ƙwayoyin ƙasa masu ƙarfi.
Zaman ƙasa sakamakon matsewa** ya ƙunshi nakasoshin roba da na filastik, da nauyin tushe ya haifar, inda a lokacin rage nauyi ƙasar ke komawa wani ɓangare zuwa asalin halinta.
Saukowa saboda matsar ƙasa ta gefe yana ƙunshe ne kawai da nakasoshin plastiki, waɗanda a lokacin rage nauyi ƙasar ba ta komawa ga yanayin farko. Suna bayyana galibi a ƙananan tushe da aka gina a ɗan ƙanƙanin zurfi a ƙarƙashin saman fili. Haka kuma, matsar ƙasa ta gefe tana faruwa a ƙasa mai sosai jika kuma wadda kusurwar gogayya ta cikinta ƙarama ce.
S obzirom na to da se dozvoljeno opterećenje tla uzima u zoni elastično plastičnih deformacija, proračun sleganja vrši se samo na osnovu smanjenja poroznosti tla pod opterećenjem, pri čemu se zanemaruju sleganja usled bočnog istiskivanja tla, koja se smatraju neznatnim.
Zaman ƙasa sakamakon matsewa ya dogara da yawan wucewar ruwa ta cikin ƙasa, domin yana faruwa ne a kan asusun ramuka, waɗanda a cikin ƙasa ta halitta koyaushe suna cike da ruwa fiye ko ƙasa da haka. Saboda haka, zaman ƙasa ƙarƙashin nauyi a gaskiya lamari ne na ruwa mai motsi, domin aikin zaman ya dogara da saurin fitar da ruwa daga cikin ramuka, inda yawan wucewar ƙasa ke taka muhimmiyar rawa.
Ƙasashen da ba su da haɗin kai kamar ƙurmi da yashi suna da manyan ƙofofi, saboda haka ƙarfin su na barin ruwa ya yi yawa, kuma ruwan da ke cikin ramuka a ƙarƙashin nauyin tushe yana fita da sauri. Don haka a cikin irin wannan ƙasa, zaunin da ke faruwa ƙarƙashin nauyin tushe yana gudana da sauri, mafi yawan lokaci tun yayin gini ko kaɗan bayan haka. Saboda haka, ba a cika ƙididdige zaunin tushe a cikin ƙasa mara haɗin kai ba.
Ƙasashe masu haɗin kai suna da ƙananan ramuka, yadda suke barin ruwa ya ratsa ba yawa ba ne kuma fitar da ruwan da ke cikin ramuka ƙarƙashin nauyin ginin tushe na iya ɗaukar lokaci mai tsawo ƙwarai, a wasu clays masu ƙananan ƙwaya har ma na tsawon shekaru goma. Bugu da ƙari, tunda jimillar porosity na ƙasa mai haɗin kai ta fi ta ƙasa mara haɗin kai yawa sosai, zama ƙasa na ƙasa mai haɗin kai ya fi yawa sosai.
A cikin ƙasa mai haɗe, wadda ramukanta aka cika da iska a wani ɓangare kuma da ruwa a wani ɓangare, fara samun saukar ƙasa ne saboda matsewar iska a cikin ramuka, yayin da yawan ruwa yake ci gaba da zama ɗaya, sannan daga baya a samu saukar ƙasa saboda tura ruwa daga ramukan. A ƙarƙashin nauyin ƙasa na tsaye saboda aikin nauyi da kuma amfani da nauyin tushe, duka waɗannan nau’o’in saukar ƙasa suna faruwa, amma tsarin lokacin saukarsu ya bambanta.
Akwai wasu dalilai ma da ke haddasa zaman ƙasa, kamar saukar da matakin ruwan ƙasa na dindindin, sauye-sauyen sinadarai a tsarin ƙasa da sauran rikice-rikice a cikin ƙasa.
Nazarin zaman ƙasa ya ƙunshi ƙididdigar zaman ƙasa na farko, wanda ake yi bisa gwajin dakin gwaje-gwaje na samfurin ƙasa da lura da zaman ƙasa, wanda ake yi a lokacin gina ginin da kuma wani lokaci bayan haka.
Lissafin zaman ƙasa a ƙarƙashin nauyin tsakiya na tushe
Mu ɗauki takalmin tushe da aka kafa a cikin ƙasa mai ƙunshe da matakai daban-daban da dama, misali layin yashi H0, wato H1 a ƙarƙashin takalmin, layin ƙasa mai laka mai kauri H2, layin yumbu mai ƙananan ƙwaya mai kauri H3, a ƙarƙashinsa akwai tsantsar ƙanƙara mai kaurin layi mafi yawa, tare da matakin ruwan ƙasa NPV (hoto 1a).
Don lissafin zaman, dole ne a zana zane na damuwa sakamakon nauyin kansa na ƙasa (zane na hagu a fig. 1b) da kuma zane na damuwa sakamakon tasirin ƙarin nauyi daga tushe (zane na dama a fig. 1b). Zanen damuwa sakamakon nauyin kansa na ƙasa ana samu ne daga kaurin yadudduka Σ_H_ da nauyinsu na kundin γ. Idan nauyin kundin yashi ne γ1, na yashi a ƙarƙashin ruwa γ’1, na ƙasar laka a ƙarƙashin ruwa γ’2, na laka a ƙarƙashin ruwa γ’3, to damuwar matsawa a ƙasa sakamakon nauyin kanta za ta kasance (fig. 1)
γ1 · H’; γ’1 · H’’; γ’2 · H2; γ’3 · H3;
Ana samun zane na matsin lamba da ke tasowa sakamakon ɗaukar nauyi ta hanyar ƙididdiga da ɗaya daga cikin sanannun hanyoyi, misali ta Steinbrenner ko Newmark, domin zurfuffuka dabam-dabam a ƙarƙashin tushe.
Idan muka nuna nauyin tushe da P, yankinsa na shimfiɗa a kan ƙasa da A, ƙimar nauyin ƙasa a zurfin kafuwa t a ƙasa da saman ƙasa da γ1, to nauyin musamman na tushe shi ne P/A yayin da nauyin ƙasar kanta a wannan zurfin shi ne γ1t. Domin a samu ƙarin nauyin ƙasa sakamakon nauyin tushe, sai a cire matsin nauyin ƙasar kanta γ1t daga nauyin tushe P/A, ta yadda ƙarin nauyin ƙasa ya zama
p0 = P/A – γ1t.
A zurfin t ɗaya kuma, damuwar γ1t saboda nauyin ƙasan ƙasa kanta tana aiki, don haka a wannan zurfin jimillar damuwa (P/A – γ1t) + γ1t, tana aiki, inda ƙarfafa ƙasan ƙarƙashin damuwar γ1t ta riga ta kammala kafin gina ginin.
Sl. 1. Kididdigar zaman ƙasa a lokacin lodin da ke tsakiyar tushe
Sai dai idan ana cika wani ɓangare na tushe da ke sama da ƙarshen tushe da ƙasa (sl. 1c), dole ne a yi la’akari da nauyin ƙasar da aka zuba 2_Q_, don haka a wannan yanayin ƙarin nauyin ya kai
_P+2_Q/A – γ1t.
Ga tushe mai siffar zani, A = b x 1,0 m a kan 1 m’ na tushe.
Ana yin lissafin zaunawa ga dukkan layukan ƙasa masu matsewa har zuwa zurfin aikin nauyin tushe. A da, ana ɗaukar iyakar aikin nauyin gini a matsayin zurfin da har yanzu damuwa na ƙarfi ≥ 10% p0 ke mamaye. A yau ana karɓar cewa wannan iyaka tana a zurfin da damuwar daga ƙarin nauyi pz ke daidai da 20% na damuwar da nauyin ƙasa kanta ke haifarwa: pz = 0,2 ·γ_Σ_H. A ƙasa da wannan zurfin ba a ƙididdige zaunawa. Bisa wata ƙa’ida ta daban, ana ba da shawarar a ƙididdige zaunawa ga layuka har zuwa zurfin 2_b_ zuwa 3_b_, inda b ita ce faɗin tushe. Idan a ƙarshe akwai layin ƙwarya kamar a sl. 1a, ba a la’akari da shi wajen lissafin zaunawa, domin zaunawarsa a ƙarƙashin nauyin tushe ba ta da yawa kuma tana faruwa ne a lokacin gini.
A zurfin z a ƙarƙashin ƙasan tushe akwai damuwar matsa lamba pg saboda nauyin ƙasa da kanta (sl. 1b), inda aka kuma la’akari da tasirin tashi mai ɗagawa. A wannan damuwar matsa lamba ta farko ana ƙara matsin pz saboda tasirin nauyin gini a wannan zurfin ɗaya. Saboda haka, a kowace ma wace maƙiƙa M a zurfin z a ƙarƙashin ƙasan tushe akwai jimillar damuwar matsa lamba pn = pg + pz.
A ƙarƙashin tasirin ƙarin nauyi, ƙasa tana zaune kuma tana samun nakasar gefe. Idan an yi watsi da nakasar gefen, saboda tana da ƙanƙanta kaɗan, tunda an yarda da nauyin ƙasa a yankin nakasassun roba-plastik, ana iya ɗauka cewa ana ƙididdige zaunin bisa gwajin matsewa a cikin edomita, tare da samfurin da ba a tauye shi ba da aka fitar daga yankin da ake nazari a cikin ƙasa, ta hanyar wane gwaji ake ƙayyade module ɗin matsewar ƙasa Ms.
Bisa ga dokar Hooke muna da
Δ_s_ = pz/Ms,
inda Δ_s_ shi ne musamman sagsawa, a kowace kauri na layi, pz damuwa a zurfin ƙasa z sakamakon ƙarin nauyi.
Idan muka ɗauka cewa kaurin layin dz ya isa ƙanana, ta yadda za a iya ɗaukar pz da Ms a matsayin masu ƙayyadaddun ƙima, to sakanin saukarwar farko zai kasance
Δ_s dz_ = pz/Ms dz.
Jimillar zaunawar layi mai kaurin H za ta kasance
Idan pZ da MS suna da ɗorewa ga layi mai kauri H, zai kasance
s = pz/Ms · H.
A gaskiya ma pz da Ms ba su dawwama ga layi mai kauri H1, sai dai ana ɗaukar matsakancinsu a cikin wurin M.
Modulin matsaƙƙen ƙasa Ms ana ƙayyade shi ta hanyar dakin gwaje-gwaje ga kowane layi daban. Ga ƙasa da aka kammala daidaitawa a al’ada, modulin Ms ana ƙayyade shi daga zanen manyan matsawa, inda jimillar nauyi σ2 = pg + pz; σ1 = pg = Σ_γt,_ ƙarin nauyi Δ_σ_ = σ2 – σ1 = (pg + pz) – pg, kuma ƙimomin da suka dace na matsawa ta dangi su ne Δ_h2_/h da Δ_h1_/h, don haka
Sai dai idan ana magana ne game da yumbu mai an riga an yi masa ƙaƙƙarfan matsawa, to ana ƙayyade ma’aunin matsewa daga zane na matsawar sakandare. Daga misalin da ke a fig. 2 muna da ga:
Hoto 2. Tantance ma’aunin matsewar ƙasa bisa ginshiƙin matsawar dangi
Daga abin da ke sama ya biyo cewa zaƙewar yumbu da aka wuce matakin haɗuwa za ta kasance ƙasa sosai fiye da zaƙewar ƙasa da aka haɗa ta al’ada.
Tasirin taurin tushe a kan zaman ƙasa
Ko da yake a aikace ba su wanzu cikakkun tushe masu sassauci, waɗanda saukar da wani wuri ba zai dogara da saukar wurin makwabta ba, a cikin ƙididdigar saukar ƙasa ana bambanta tushen masu sassauci da tushen masu ƙarfi.
Tushe masu ɗan sassauci, wato tarin duwatsu da cike-cike na ƙasa, suna haifar da zaman ƙasa daban-daban a wasu wurare idan nauyi ya kasance daidai. Saboda haka, a waɗannan tushe ba a yin ƙididdigar zaman ƙasa ga dukan saman da aka ɗora nauyi a kai, sai dai ga wasu wurarensa: kusurwoyi A, B, C da D, maki na tsakiya na gefuna E, F, H da J da kuma tsakiyar saman murabba’i G (sl. 3). A lokacin ɗora nauyi daidai, zaman maki B, C da D ya yi daidai da na maƙi A, zaman maƙi H ya yi daidai da na maƙi E, maƙi J ya yi daidai da na maƙi F ga ƙasa mai irin wannan haɗin.
Hot. 3. Ƙididdigar zaunarwar wasu wurare na saman da aka ɗora nauyi
Domin a ƙididdige nakasar a ƙarƙashin kowace aya G ta saman da aka ɗora wa nauyi, a raba murabba’in kusurwa ABCD zuwa manyan murabba’ai huɗu ƙanana, sannan nakasar G tana samuwa a matsayin jimillar nakasoshin da kowane daga cikin murabba’ai da aka raba ya haifar.
Tushe masu ƙauri ba sa nutsewa iri ɗaya da masu sassauci, domin a gare su ba zai yiwu wasu wurare su nutse dabam-dabam ba. Saboda haka, ana ƙididdige nutsewar tushe masu ƙauri a matsayin ɗaya gaba ɗaya, amma ana ƙayyade matsakaicin nutsewa ta wata hanya dabam gwargwadon matakin ƙaurin, domin rabon matsin lamba a ƙasan tushe yana dogara da ƙaurin tushe.
Ga tushe masu tsauri masu siffar murabba’i ko ƙaramin murabba’i mai ɗan faɗi, inda a < 2_b_, ana ƙididdige zaman ƙasa sG na tsakiyar G kuma a ɗauki zaman ƙasa na gaba ɗaya na tushe s = 3/4 sG. Ga tushe masu tsauri masu siffar murabba’i mai tsawo ko layi, ana ƙididdige zaman ƙasa na ƙarshen E, tsakiyar G da kuma ma’anar M a rabin tazara tsakaninsu, a kan doguwar axis ta ƙafar tushe, sannan a ɗauki matsakaicin ƙima.
Van Hamme yana ganin cewa mafi daidai lissafin zaunarwa shi ne na „maɓallin nuni P“, wanda ke nesa da manyan igiyoyi da tazara
daga manyan axis na tsakiya. Bisa ga Van Hamme, zaman ƙasa na wasu takamaiman wurare na tushe ba ya dogara da hanyar rabon damuwa a ƙasan tushe. Ga waɗannan wurare, ana iya ƙididdige zaman ƙasa bisa zato cewa rabon damuwa a ƙasan tushe daidai yake a ko’ina. Ga ƙafar tushe mai tsauri, wadda aka ɗora da nauyi daidai a saman ta amma rabon damuwa a ƙasan tushe ba daidai ba ne kuma yana ƙaruwa zuwa gefunan ƙafar, duk da haka zaman ƙafar tushe daidai yake da zaman muhimmin wuri P. Damuwa a zurfin z a ƙarƙashin muhimmin wuri P na fili mai murabba’i mai tsawon a, faɗi b, wanda aka ɗora masa nauyi daidai p0 za a iya ƙididdige su ta amfani da teburin 1 da Jelinek ya tsara.
Damuwa σzP a zurfin z a ƙarƙashin maɓallin musamman P ita ce σzP = (σz/p0)·p0, inda p0 ƙarin nauyin ƙasa ne.
Teb. 1. Ƙimomin σz/p ga matsalolin da ke ƙarƙashin muhimmin batu P dangane da rabon zurfin z zuwa faɗin b da kuma rabon tsawo a zuwa faɗin b na sawar tushe
Proračun sleganja na osnovu promene koeficijenta poroznosti tla
Idan muka yi wa e0 alama a matsayin ma’aunin porosity na samfurin da ba a taɓa shi ba da aka fitar daga layin ƙasa, kuma ei a matsayin ma’aunin porosity na wannan samfurin bayan kammala haɗaɗɗen matsawa a cikin edometer ƙarƙashin nauyi σ1 (sl. 4a), raguwar ƙarar farko ta ƙasa ƙarƙashin tasirin nauyi Δ_σ_ tana daidai da raguwar porosity, wato ma’aunin porosity na ƙasa
Δ_e_ = e0 – e1
Sl. 4. Proračun sleganja na osnovu promene koeficijenta poroznosti tla
Matsayin farko na ƙarar samfurin ƙasa shi ne
Nutar nutsewa ta musamman Δ_s_, wato nutsewa a kowace naúrar ƙarar ƙasa 1+e0 shi ne
Δ_s_ =(e0–e1) / (1+e0)
Zaƙewar matakin ƙasa na asali mai kaurin dz ya kasance, kamar yadda aka nuna a fig. 4b
Δ_s_ dz=(e0–e1) / (1+e0) dz
Zirga-zirgar Layer mai kaurin H za ta kasance
Idan muka ɗauka cewa p matsin lamba ne a zurfin z saboda nauyin ƙasa na kanta, wanda ya yi daidai da nauyin σ0 a edometer, Δp kuwa matsin lambar ƙarin kaya na ƙasa sakamakon gini, wanda ya yi daidai da ƙarin nauyi Δ_σ_ a edometer, kuma p1 jimillar matsin lamba ƙarƙashin tasirin nauyin ƙasa na kanta da ƙarin kaya wanda ya yi daidai da jimillar kaya σ1 a edometer, za mu iya rubuta tsarin gaba a siffar
Idan muka ayyana A a matsayin yankin zane na damuwa daga ƙarin nauyin ƙasa, A = Δ_pH_ (yankin da aka yi inki a sl. 4b), inda Δ_p_ shi ne damuwa daga ƙarin nauyi a tsakiyar layi
a=Δ_e_/Δ_p_, dangantakar bambancin ƙimar porosity da matsin da ya dace daga ƙarin nauyi Vc = (1+e0)/a, za mu iya sanya
wato s = A/Vc [cm]
Idan ƙasa ta ƙunshi yadudduka da yawa, ana ƙididdige zaman s ga kowane yadi; tarin zaman kowane yadi yana ba da jimillar zaman Σ_s_.