Ike ibu ala

N’ime mekanik nke ala, a na-ekpebi ike ibu kacha elu nke ala na ibu a na-ekwe ka ala were.

Ike ibu kacha elu nke ala bụ nke a na-eru mgbe mmebi ala malitere. Mmebi ala na-apụta mgbe ibu nke ntọala na-arụ na ala karịrị ike ya iguzogide ịkpụgharị. N’ọnọdụ a, n’okpuru mmetụta ibu ntọala P apụta elu nwere nguzogide kacha nta ACD na BCE – elu mmịfe fig. 1, nke ala na-amịpụ n’akụkụ, ma n’otu oge a na-ahụkwa ibili nke ala n’elu elu teren n’akụkụ ụlọ DG na EF, ebe ntọala n’onwe ya na-adaba.

Sl. 1. Mmebi ala n’okpuru mmetụta nke ibu ntọala

Ike igbutu nke ala na-abawanye ka omimi ntọala t na-abawanye, n’ihi na, n’ihi ịdị arọ nke oyi akwa dị n’elu, ohere nke ịkpọpụ ya n’akụkụ na-ebelata. Ya mere, ntọala miri emi na-akpalite mmebi ala n’ụzọ siri ike karị, ebe ntọala na-adịghị omimi dị ize ndụ n’ihe gbasara mmebi. N’otu aka ahụ, ntọala sara mbara na-akpalite mmebi ala n’ụzọ siri ike karị, n’ihi na elu ịsọgwụ dị omimi karịa.

Ibu a na-ekwe ka nke ala bụ nke a pụrụ ikwe ka ọ rụọ ọrụ n’ala n’ụzọ na-agaghị akpata mgbaji nke ala n’okpuru ọnọdụ kachasị njọ enwere ike. A na-ekpebi ibu a na-ekwe ka ala site n’ịdabere na ikike ibu ikpeazụ nke ala site n’iji ihe nchekwa. Ogo nke ihe nchekwa na-adabere na ọtụtụ ihe, nke kachasị mkpa bụ ịdị ziri ezi nke njirimara anụ ahụ nke ala, ohere mgbanwe nke ụkpụrụ nke ihe ndị na-eguzogide n’ime ala, karịchaa cohesion, nke uru ya nwere ike ịgbanwe n’oke sara mbara n’ọrụ mmiri dị n’ala, mgbe ahụ mmetụta nke ihe ndị ọzọ nwere ike ịdị, dị ka ọnọdụ ibu (ụlọ ọrụ ibu mberede na nke dinamik), omimi ntọala, na obosara nke ụkwụ ntọala.

A pụrụ ikpebi ikike ibu ala dabere na mmebi ala, nke na-enye ikike ibu oke. N’okpuru ikike ibu oke nke ala, a na-aghọta ọnụ ọgụgụ ibu nke na-akpata mmebi. E nwere ụzọ abụọ e si achọpụta ikike ibu oke dabere na mmebi ala, ya bụ ngwọta mgbakọ na mwepụ na ibu nnwale.

Ngwọta mgbakọ

Ọtụtụ ndị ọkà mmụta sayensị gbalịrị ịchọta ngwọta mgbakọ na mwepụ iji kpebie ikike ibu kacha elu nke ala, dabere na ịmata ihe ndị na-emetụta ya na n’okpuru echiche dị iche iche nke ọnọdụ mmebi. Ihe ndị na-emetụta ya bụ àgwà anụ ahụ nke ala, nke a na-ekpebi site na ule ụlọ nyocha n’elu ihe atụ ala na-adịghị emebi emebi, ọnọdụ mmiri ala, omimi nke ntọala, nha na ọdịdị nke elu a na-ebu ibu, yana ụzọ e si etinye ibu, ya bụ ibu hà nhata ma ọ bụ na-adịghị hà nhata, etiti ma ọ bụ nke na-apụ n’etiti nke ala. Echiche banyere ọnọdụ mmebi dabere na tiori plastisiti na tiori elasticiti. Otú ọ dị, ụzọ oge a si ekpebi ikike ibu nke ala na-adabere na tiori plastisiti, nke a na-ejikọta na ụfọdụ echiche dị mfe.

N’ebe a, anyị ga-eweta ụzọ mgbakọ a maara nke ọma ole na ole maka ikpebi ikike ibu kachasị elu, ya bụ ibu a na-ekwe ka ala kwado.

Ụkpụrụ Prandtl-Caquota

Ọ bụrụ na a tọrọ ụkwụ ntọala AB n’omimi t n’okpuru elu ala, n’omimi a nrụgide kọntaktị po na-adị n’ihi ibu ntọala, na nrụgide akụkụ p=γt na-adị n’ihi ịdị arọ ala dị n’elu ọkwa ụkwụ ntọala ruo n’elu ala (sl. 2).

N’okpuru mmetụta kpọmkwem nke ịdị arọ ntọala, n’oge a gafere ike ibu ala nke ọma, apụta elu mwepụ kpọmkwem AC na BC, nke na-emepụta akụkụ α = 45° + ϕ/2 na elu a na-eburu ibu. Elu mwepụ ndị a na-emepụta prism ala na-arụ ọrụ ABC.

Sl. 2. Elu mmịfe nke ụdị okirikiri logarithm n’okpuru mmetụta nke nkwụnye ụkwụ ntọala e mere ka ibu ya bụrụ nke etiti dịka Prandtl-Caquot

N’okpuru mmetụta nke nrụgide nke prizm ala nọ n’ọrụ, prizm ala pasif n’akụkụ ADD1 na BEE1 na-apụta, nke ọ na-agbalị ịkụgharị elu n’elu elu slide DD1 na EE1, n’akụkụ 45°-ϕ/2 na horizontaal. N’etiti mpaghara nrụgide ala nọ n’ọrụ na nke pasif, e nwere mpaghara ịkpụ radialis ACD ma ọ bụ BCE, nke n’ime ya, mgbe a gafere nguzozi oke, slide na-eme n’elu elu slide gbagọrọ agbagọ. Résal gbakọrọ na elu slide dị na mpaghara ịkpụ radialis dị n’ụdị spiral logarithmic nwere pole na A ma ọ bụ B, nke nha ya bụ r=r0 eπ tg_ϕ_

Iji kpebie ibu oke nke ala, e mere echiche ndị a:

• na ntọala dị larịị, ya bụ na a na-eleghara esemokwu dị n’etiti ụkwụ ntọala na ala anya;
• na ike ịkpụ nke ala n’akụkụ elu D1M na E1N adịghị, ya bụ, a na-eleghara ya anya;
• na ịdị arọ olu nke ala n’okpuru isi ntọala γ=0, ya bụ, a naghị atụle mmetụta nke ịdị arọ nke ala n’okpuru ụkwụ ntọala, n’ógbè nhata plastik.

Ụdị Prandtl-Caquota bụ:

Ike ibu nke ala ruru oke bụ

Ọ bụrụ na anyị tinye:

oke ibu ibu nke ala jikọrọ ọnụ bụ qf = γtm + cm1.

Maka ụkpụrụ dị iche iche nke akụkụ ọkụ n’ime ala, ụkpụrụ maka m na m1 dị na tebụl 1.

Tabl. 1. Uru nke ọnụọgụ m na m__1 maka ụkpụrụ dị iche iche nke akụkụ esemokwu ime nke ala

Ibu ala a kwere ka ọ nagide bụ qa = pdozv = qf/F ebe F bụ ihe nchekwa. Maka itinye usoro Prandtl-Caquot, a na-ewere F = 4, ya mere qa = qf/4.

Usoro Terzaghi

Terzaghi nyere usoro semi-empiirik maka ịgbakọ ikike ibu kacha elu nke ala n’okpuru mmetụta ibu nke ụdị ọkpọ, square na efere okirikiri. Ọ lere ntọala nke e hiwere na omimi Df n’okpuru elu ala, nke obosara B (sl. 3), ma nabata na e nwere esemokwu n’etiti isi ntọala AB na ala, nke na-emegide ịpụpụ ala n’akụkụ, nakwa na ebe ịkụda AB na BC na-eme oghere nke esemokwu ime na elu e bu ibu.

Sl. 3. Ike ikpeazụ nke ala dịka Terzaghi si kwuo

N’ihi nke a, ala dị na akpụkpọ ụrọ ABC, nke dị n’etiti ntọala AB na elu mgbagharị AC na BC na-anọ n’ọnọdụ nhata nke elastic ma na-eme dịka akụkụ nke ntọala. Prizim ABC enweghị ike ịkwaga ruo mgbe nrụgide dị n’akụkụ ya AC na BC ga-adaba na nrụgide ala pasiv nke prisim dị n’akụkụ, nke pụtara na mgbe e gabiga ọnọdụ oke nke nhata, nrụgide ala na-esite na ya q na-arụ ọrụ n’akụkụ ikuku ϕ megide normal na elu mgbagharị, ya bụ n’ụzọ kwụ ọtọ (sl. 3). Ebe akpụkpọ ahụ na-agagharị n’ihu n’ala n’okpuru mmetụta ibu, nsogbu nhata dị n’ala na-agbadata n’ikpebi nrụgide ala pasiv. Agbanyeghị, ebe ngụkọta ziri ezi nke ikike ibu ala site n’ụzọ a dị mgbagwoju anya, Terzaghi nyere ngwọta dị mfe. Usoro Terzaghi maka ịgbakọ ikike ibu oke nke ala _q_f bụ

1. Maka ụkwụ ntọala nke ụdị eriri

qf = cNc + γ1 DfNq + 0,5 γ2 BNγ  

ebe c bụ njikọta nke ala

γ1 ịdị arọ olu nke ala dị n’elu ntọala

Df omimi nke ịtọ ntọala n’okpuru elu ala ruo n’okpuru ntọala

γ2 ịdị arọ olu nke ala dị n’okpuru ụkwụ ntọala

B obosara nke ntọala ụkwụ.

Nc, Nq, Nγ bụ ihe atụ ibu iburu, na-adabere na akụkụ nke esemokwu ime n’ala; usoro maka ihe ndị a bụ ndị a:

Nq bụ ihe kpatara ịdị arọ nke oyi akwa ala dị n’akụkụ ruo omimi nke ntọala: Nq = tg2 (45° + ϕ/2) eπ tg_ϕ_

Nc bụ ihe kpatara n’ihi cohesịon: Nc = (Nq – 1) ctg_ϕ_

Nγ bụ ihe kpatara n’ihi ịdị arọ nke ya nke mkpụrụ ala n’okpuru footing, ya bụ n’okpuru obosara footing AB. Brinch Hansen na-atụ aro uru nke ihe kpatara a dịka ihe dị nso: Nγ ≈ 1,8 (Nq – 1) tg_ϕ_

Sl. 4. Nkesa nrụgide nke ala na-enweta mgbe a na-etinyere ibu etiti kwụ ọtọ na ntọala

N’ihi obere ọdịiche dị n’arọ olu ala, a na-anabatakarị γ1= γ2= γ. Dika nha nke dị n’ihu si egosi, ikike ibu ala na-adabere (sl. 4) n’ihe ndị a: njikọ nke ala ntọala c, ibu ala n’akụkụ ntọala γ1 D_F, na ibu nke ala nke prism na-awagharị n’onwe ya nke obosara B.

Ma ebe nkesa nrụgide nke ala na-enweta n’ihi mmetụta nke njikọ c na omimi ntọala Df bụ otu n’ofe obosara dum, ya bụ akụkụ anọ, n’aka nke ọzọ nkesa nrụgide nke ala na-enweta n’ihi mmetụta obosara B bụ akụkụ triangle, ya bụ nrụgide kachasị elu na-anabata n’etiti ntọala, ma na-ebelata n’akụkụ ebe ha hà efu.

Sl. 5. Ihe ngosi nke ihe ntụgharị ibu dabere na akụkụ nke esemokwu ime ala dịka Terzaghi si kwuo

Maka uru dị iche iche nke akụkụ site na 0 ruo 40°, Terzaghi haziri eserese nke ihe na-eburu ibu (sl. 5). Otú ọ dị, ihe na-eburu ibu Nc, Nq na Nγ (ahịrị zuru ezu na onyonyo 5) enwere ike ịnakwere naanị n’ọnọdụ ala siri ike ma kpọkọtara nke ọma. Ọ bụrụ na ala ahụ dị nro ma ọ bụ na-ehulata nke ukwuu, mgbe ahụ a ga-anabata ihe na-eburu ibu N’c, N’q na N’γ (ahịrị ntụpọ na sl. 5), nke na-enye 2/3 nke uru nguzogide esemokwu. Na mgbakwunye, n’ọnọdụ a a ga-ewere 2/3 nke njikọ c enwetara n’ụlọ nyocha, ya mere n’okwu a anyị nwere qf = 2/3 cN’c + γ1 DfN’q + 0,5 γ2 BN’γ.

2. Maka ụkwụ ntọala nke ụdị akụkụ anọ

qf = 2/3 (1+0,3 B/L) cN’c + γ1 DfN’q + 0,5 γ2 BN’γ  ebe L bụ ogologo nke ntọala ụkwụ

3. Maka ntọala ala nke ụdị square

qf = 2/3 1,3 cN’c + γ1 DfN’q + 0,4 γ2 BN’γ  

4. Maka ntọala okirikiri

qf = 2/3 1,3 cN’c + γ1 DfN’q + 0,6 γ2 rN’γ  ebe r bụ radius nke ntọala ụkwụ.

Maka mgbakọ ibu ala kwekọrọ, a na-ewere faktor nchekwa F: qa = qf/F. Uru nke faktor nchekwa na-agbanwe site na 2 ruo 3 dabere na ọnọdụ ala na ibu.

Ojiji nke usoro mgbakọ na mwepụ

Iji jiri usoro mgbakọ na mwepụ chọpụta ibu a na-ekwe ka ala nabata, ọ dị mkpa ịmata àgwà geomechanical nke ala, ya bụ, njikọta na esemokwu ime n’omimi ntọala, yana ịdị arọ olu nke ala dị n’elu na n’okpuru ụkwụ ntọala. Ọ bụrụ na ala ntọala dị n’okpuru ọkwa mmiri ala, a ga-atụlekwa nrụgide ebuli elu n’ịkọwapụta ịdị arọ olu nke ala.

N’ọnọdụ ibu ala buru ibu na nnukwu ihe owuwu, mgbe uru enwetara nke ibu ala a kwere ekwe dabere na usoro mgbakọ na mwepụ ejirila kpamkpam, mgbakọ nke ike ibu nke ala kwesịrị iso ya na mgbakọ nke mmebi ịda ala. A na-anabata ike ibu ala a gbakọrọ naanị mgbe mgbakọ nke ịda ala gosipụtara ịda ala dị nta karịa nke a kwere ekwe maka ụdị ihe owuwu ahụ. Ọ bụrụ na mgbakọ gosipụtara ịda ala karịrị nke a kwere ekwe, a naghị anabata uru a gbakọrọ nke ibu ala a kwere ekwe site n’ụkpụrụ mgbakọ, kama a ga-agbanwe ụzọ e si wuo ntọala ka e wee nweta ịda ala dị nta, n’ime oke ịda ala a kwere ekwe maka ụdị ihe owuwu ahụ.

Fig. 6. Omimi ntọala dị irè D__f

N’ihe atụ mgbakọ nke iji chọpụta ikike ibu ala nke oke, a naghị eburu n’uche esemokwu nke mkpuchi ntọala, nke na-esokwa dị ka nguzogide megide mmetụta ibu, ma ọ bụrụ na ntọala ahụ na-emetụ ala nke ọma n’akụkụ akụkụ. E kwesịghị iburu nguzogide esemokwu nke mkpuchi n’uche, n’ihi na ezi esemokwu nke mkpuchi dị naanị n’ụzọ nke piles a na-akụ n’ime ala, ebe n’ụkwụ ntọala esemokwu nke mkpuchi adịghị mkpa, n’ihi na a na-arụ ụkwụ ntọala n’ime olulu e gwuru tupu oge eruo.

Iji usoro mgbakọ na mwepụ nke na-adịghị ele ụdị ntọala anya na-enye nsonaazụ kacha nso maka ntọala ụdị teepu, ya bụ mgbe ogologo ntọala karịrị obosara ya ugboro abụọ. Nnyocha egosila na, n’aka ntọala ụdị square ma ọ bụ okirikiri, mgbaji na-eme n’ibu ókè nke dị 10-30% karịa nke a gbakọtara site na usoro mgbakọ na mwepụ. Ntọala atọ akụkụ na-enye ibu ibu pere mpe karịa nke teepu, ebe ibu kacha nta bụ nke ntọala ụdị mgbanaka, ma ọ bụrụ na e mejupụtaghị ha.

A na-agbakọ omimi ntọala Df dịka omimi ọrụ nke ntọala n’okpuru ala nke isi ntọala ruo n’ala ntọala (Sl. 6). N’ebe ntọala dị n’okpuru ọnụ ụlọ dị n’okpuru ala, omimi ọrụ Df dị iche na omimi ntọala kwa n’okpuru elu ala. N’ọnọdụ ndị dị otu a, maka ịgbakọ oke ibu na ibu a na-ekwe ka ala kwado, a ga-eji Df mgbe niile, ebe n’elu ala nke isi ntọala enwere ikuku nke na-adịghị eguzogide ịpụgharị ala n’akụkụ n’okpuru mmetụta ibu ntọala P.