Idan muka yanke silinda a cikin ƙasa mai ɗaure sannan muka sa shi ƙarƙashin aikin matsin lamba na al’ada P (sl. 1), sabbin matsaloli za su bayyana a cikin silindar, wato matsin tsaye na lamba σ da matsin yanka na kwance. Idan muka ƙara matsin P a hankali, bayan wani lokaci za su bayyana a kan silindar wani fashewa mai karkace, sannan nan take silindar zai karye. A lokacin karyewar, silindar ya yi karkace ƙarƙashin aikin matsin P kuma a kan hanyar yanka ta mafi ƙarancin juriya N-N.
Hoto. 1. Tasirin matsin lamba a kan silinda da aka cire daga ƙasa mai haɗuwa
Juriyar ƙasa da silinda ya nuna wa ƙarfin P a lokacin karyewa ana kiranta juriyar yanke ƙasa, kuma kusurwar α na karkatar da matakin ƙaramin juriya zuwa layin kwance ana kiranta kusurwar matakin ƙaramin juriya na yanke ƙasa.
Juriya ga yanka na ƙasa mai haɗe tana ƙunshe da abubuwa biyu na asali: gogayya ta ciki tsakanin ƙwayoyin ƙarfi da haɗin kai wanda ke ɗaure ƙwayoyin ƙarfi. Ana ɗaukar ƙarfin yanka na ƙasa daidai da mafi girman matsin yanka a lokacin karyewa kuma ana bayyana shi da daidaito
τf = c + σ tg_φ_
inda: τf ƙarfin yankan ƙasa [kp/cm2],
c haɗin ƙasa [kp/cm3],
σ matsin lamba na ƙasa [kp/cm3],
φ kusurwar gogayyar cikin ƙasa.
Masanin Faransa Coulomb ne ya ba da wannan dabara a shekara ta 1785. Bisa ga wannan dabara, ga ƙasa da aka bayar haɗin kai c yana da ɗorewa kuma ba ya dogara da matsin lamba na al’ada, yayin da juriyar gogayya σ tg_ϕ_ take daidai gwargwado da damuwa σ. A zahiri, haɗin kai e ba ya kasancewa ɗorewa ga ƙasa da aka bayar, sai dai ita ma tana dogaro da wani ɓangare da damuwar al’ada σ, domin ƙarƙashin wannan matsin lamba kaurin fim ɗin ruwa da ke rufe ƙwayoyin ƙarfi yana raguwa, ta haka haɗin kai yana ƙaruwa. Dabarar Coulomb tana aiki ga ƙasashen da ruwa ke ratsa su, inda ƙarƙashin matsin lamba na al’ada ruwa daga ramukan ƙasa yake fita ba tare da matsala ba, kamar yadda yake a ƙasa mai tsakuwa da yashi, amma ba haka ba ne a ƙasa mai haɗi, wadda ba ta da sauƙin ratsa ruwa, don haka ruwa daga ramuka yana fita da wahala kuma yana rage a matsayin ruwa na pore mai matsa lamba ƙarƙashin nauyin P.
Matsin lamba mai tasiri da na tsaka-tsaki a ƙasa
Sl. 2. Matsin lamba mai inganci da na tsaka-tsaki a cikin ƙasa
Idan muka sa samfurin ƙasa a ƙasan kwantena, misali yashi busasshe, kuma muka ɗora masa wani nauyi, misali ƙwayoyin gubar ƙanana masu nauyin W, dukan nauyin wannan zai ɗauke shi ƙwayoyin ƙasan. Matsin lamba na musamman a saman samfurin p0 = W/A a kp/cm3, inda A yake nufin yankin sashin samfurin, zai haddasa kamewar samfurin, wato rage porosity ɗinsa, amma kuma zai haifar da sauye-sauye a sauran kaddarorin jiki na samfurin kamar ƙaruwa a ƙarfin yankewa, ƙaruwa a modulin matsewa da sauransu. Matsin lamba da ke tsakanin saman haɗuwar ƙwayoyi ana kiransa matsin lamba mai tasiri ko matsin lamba tsakanin ƙwayoyi σ’. Idan an samu haɗuwar ƙasa wato samfurin ya daina zama yana raguwa a ƙarƙashin nauyin p0, matsin lamba mai tasiri ya zama daidai da jimillar matsin lamba na musamman da ke aiki a zurfin da ake nazarin ƙasar. A wannan hali, a zurfin da ke ƙasa da saman samfurin a sl. 2 σ’ = W/A + hzγ inda γ yake nauyin ƙasa na samfurin.
Sai dai idan muka ɗora samfurin a cikin akwati da ruwa maimakon ƙwallayen gubar har zuwa tsayin h, tare da cewa ruwan ya cika dukkan ƙofofin samfurin, matsin ginshikin ruwa a sama da samfurin hγw, inda γw shi ne nauyin girman ruwa, ba zai haifar da zaunewar samfurin da rage porosity dinsa ba kuma ba zai ƙara ƙarfinsa na yanka da ma’aunin matsewa ba. Saboda haka ake kiran matsin hydrostatic hγw da suna matsi na tsaka-tsaki. Matsi na tsaka-tsaki da ake alama da u yana yaduwa cikin samfurin a dukkan fannoni da daidai ƙarfi. Wannan matsin ba zai haifar da ƙaruwa a ƙarfin yanka ba, domin ruwa kansa ba shi da kowace irin ƙarfin yanka.
Saboda haka matsin lamba mai tasiri σ’ yana wucewa ta wuraren hulɗa tsakanin ƙwayoyin ƙasa masu ƙarfi, yayin da matsin lamba na tsaka-tsaki u yake wucewa ta cikin ruwan da ke cikin ramuka. Idan ɓangaren ƙasan akwati ya cika da samfurin ƙasa mai cikakken ruwa wanda nauyin sa na girma shi ne γz, kuma sama da saman samfurin har zuwa matakin N akwati ya cika da ruwa wanda nauyin sa na girma shi ne γw, to jimillar matsin lamba σ a kowace wurin samfurin zai kasance σ = σ’ + u.
A zurfin hz, a ƙarƙashin saman samfurin matsin lamba mai amfani zai kasance σ = σ’ - u
inda σ = h γw + h γz
u = (h + hz) γw.
Don haka zai kasance σ’ = hz γ’
γ’ ita ce nauyin girma na ƙasa da aka nitse cikin ruwa.
Babbar ma’aunin ƙarfin jure yankewar ƙasa
Idan muka ɗora ƙasa mai ɗaurewa da nauyi P, wannan nauyin zai haifar da zaunawar ƙasa kuma da fari za a fitar da iska daga cikin ramuka a ƙarƙashin tasirinsa, har zuwa lokacin da nan da nan ruwa kaɗai zai rage a cikin ramukan. Saboda ƙarancin yadda ƙasa mai ɗaurewa ke barin ruwa ya wuce, ruwan ba zai iya fita nan take ba, don haka yana nan a matsayin ruwa mai matsawa a cikin ramukan kuma da farko yana ɗaukar jimillar nauyin waje P. A ci gaban lokaci na gaba, ƙarƙashin tasirin nauyin P ruwa yana fara ficewa daga ramuka, kuma ƙwayoyin ƙarfi suna kusantar juna, su kuma yanzu suna ɗaukar wani ɓangare na nauyin P. A nan muna da τf =c + (σ - u) tg_ϕ,_ inda σ shi ne jimillar matsa lamba daga nauyin P, u matsin ruwan ramuka.
Matsin lambar ruwan ramuka u ya dogara da abubuwa da dama, kamar yanayin lokacin haɗewar ƙasa, yawan wucewar ruwa a cikin ƙasa, girman nauyin da ke kan ƙasa da sauransu. Ƙarfin yankewar ƙasa ya dogara da matsin lambar ruwan ramuka kuma ya fi girma a u=0, lokacin da haɗewar ƙasa ke faruwa.
Aikin colloid na ƙasa
Abubuwan juriya na ciki na ƙasa cohesion da friction na iya bambanta kuma suna dogara sosai da girman ƙwayoyin ƙasa masu ƙarfi da siffofin robarsu. Domin tantance tasirin cohesion idan aka kwatanta da juriya na cikin gida na ƙasa mai haɗuwa, Skempton ya gabatar da ra’ayin aikin colloidal na ƙasa _K_P, wanda aka nuna da dangantakar ma’aunin robobi IP da yawan ƙwayoyin da suka fi ƙanƙanta da 0,002 mm cikin % na nauyin dukan taro. A nan an ɗauki wannan ƙa’ida (sl. 3):
Sl. 3. Ayyukan colloidal na ƙasa
Ga KP < 0,75 akwai yumbu marasa aiki,
ga KP = 0,75 – 1,25 su ne yumbu na al’ada,
ga Kp > 1,25 na gilin aiki.
Tare da ƙaruwa KP, tasirin haɗin kai yana ƙaruwa idan aka kwatanta da gogayen cikin gida na ƙasa mai haɗin kai.
Tausayin ƙasa
Idan a cikin ƙasa mai haɗin kai muka fitar da silinda mai diamita 3—3,4 cm da tsawon ~ 5 cm sannan muka ɗora masa nauyin normal, a lokacin da silindar ta karye za mu samu ƙarfin matsa lamba na ƙasa a yanayin da bai lalace ba σ__ₙ:
σn = P/A a kp/cm2,
inda A shi ne sashen giciye na silinda.
Bayan an gama gwajin, samfurin da ya karye ana mayar da shi sannan a sake ƙera silinda mai girma ɗaya, ta amfani da wannan sinadarin-mold ɗin, tare da a bar danshinsa ya kasance kamar yadda yake a gwajin da ya gabata. Sai a nan take bayan an ƙera silinda ɗin da aka sake daddagewa a sake yin gwajin da shi, ta yadda za a samu ƙarfin matsawar ƙasa a cikin yanayin da ya rikice σ__ₚ.
Hankali (sensitivitet) S__ₜ shi ne dangantakar ƙarfin matsawa a yanayin da ba a damtsa ba da ƙarfin matsawa a yanayin da aka damtsa: St = σn/σp,
Bisa wani ma’auni, ana kimanta saurin amsawar S__ₜ kamar haka:
- ga S__ₜ = 1 — 2 akwai ƙarancin saurin gano laushin yumbu,
- ga S__ₜ = 2 — 4 ita ce matsakaiciyar hankalin laka,
- ga S__ₜ = 4 — 8 akwai babbar saurin amsawar ƙasa,
- ga S__ₜ > 8 yumbu ne mai matuƙar taushi.
A cikin yanayi kan faru cewa sakamakon tasirin inji, misali girgizar ƙasa, ƙasa mai laka ta rasa ƙarfinta kwatsam, sannan daga baya ta sake samunsa a lokacin da take a hutawa. Ana kiran wannan hali tiksotropiya ta ƙasa. Yawancin lakan suna da halayen tiksotropiya a wani mataki. An san lokuta na zamewar gangaren ramuka sakamakon malalar laka mai tiksotropiya a Norway, Sweden da Finland, inda bincike ya tabbatar da cewa babu canjin danshin laka a lokacin wannan aikin, wato danshin laka ya kasance daidai kafin da bayan malalar.