{"id":22695,"date":"2022-06-13T11:17:09","date_gmt":"2022-06-13T09:17:09","guid":{"rendered":"https:\/\/www.geostru.eu\/ro\/analisi-di-stabilita-dei-pendii\/"},"modified":"2022-12-02T07:38:32","modified_gmt":"2022-12-02T06:38:32","slug":"stabilitatea-taluzurilor","status":"publish","type":"post","link":"https:\/\/www.geostru.eu\/ro\/blog\/2022\/06\/13\/stabilitatea-taluzurilor\/","title":{"rendered":"Stabilitatea taluzurilor"},"content":{"rendered":"<div class=\"wpb-content-wrapper\"><p>[vc_row][vc_column][vc_column_text]<\/p>\n<h3 style=\"text-align: justify;\"><strong>Stabilitatea taluzurilor <\/strong><\/h3>\n<p>Taluzul este o suprafat\u00e3 \u00eenclinat\u00e3 cu panta, \u00een general, mai mare de 45\u00b0, realizat\u00e3 \u00een special antropic, care m\u00e3rgineste un rambleu sau un debleu. Alunec\u00e3rile de teren sunt o categorie de fenomene naturale de risc, ce definesc procesul de deplasare, miscarea propriu\u2011zis\u00e3 a rocilor sau depozitelor de pe versanti, c\u00e2t si forma de relief rezultat\u00e3.<\/p>\n<h3 style=\"text-align: justify;\"><strong>Introducere \u00een analiza stabilit\u00e3tii<br \/>\n<\/strong><\/h3>\n<p style=\"text-align: justify;\">Rezolvarea problemei stabilit\u00e3tii necesit\u00e3 luarea \u00een considerare a ecuatiilor de echilibru si a leg\u00e3turilor constitutive (ce descriu comportamentul terenului). Aceste ecuatii sunt foarte complexe \u00eentruc\u00e2t terenurile sunt sisteme multifazice, care pot fi readuse la forma sistemelor monofazice numai \u00een conditii de teren uscat sau analiz\u00e3 \u00een conditii drenate.<br \/>\n\u00cen cea mai mare parte a cazurilor avem de-a face cu un material care, dac\u00e3 este saturat este cel putin bifazic, ceea ce \u00eengreuneaz\u00e3 utilizarea ecuatiilor de echilibru. Este practic imposibil\u00e3 definirea unei legi constitutive cu valabilitate general\u00e3 \u00eentruc\u00e2t terenurile prezint\u00e3 un comportament non-linear cu mici deformatii, sunt anizotrope iar comportamentul lor depinde at\u00e2t de efortul deviator c\u00e2t si de cel normal.Din cauza acestor dificult\u00e3ti se introduc ipotezele simplificante:<\/p>\n<ol style=\"text-align: justify;\">\n<li>Se folosesc legi constitutive simplificate (modelul rigid perfect plastic). Se presupune c\u00e3 rezistenta materialului este exprimat\u00e3 numai prin parametrii coeziune (c) si prin unghiul de frecare intern\u00e3 (\u03c6), constante pentru teren, si caracteristici st\u00e3rii plastice. Deci se presupune valid criteriul de cedare Mohr-Coulomb.<\/li>\n<\/ol>\n<ol start=\"2\">\n<li style=\"text-align: justify;\">\u00cen unele cazuri sunt satisf\u00e3cute numai partial ecuatiile de echilibru.<\/li>\n<\/ol>\n<h4 style=\"text-align: justify;\"><strong>Metoda echilibrului limit\u00e3 (LEM)<\/strong><\/h4>\n<p style=\"text-align: justify;\">Metoda echilibrului limit\u00e3 const\u00e3 \u00een studiul echilibrului unui corp rigid, constituit din taluz si dintr-o suprafat\u00e3 de alunecare de form\u00e3 oarecare (linie dreapt\u00e3, arc de cerc, spiral\u00e3 logaritmic\u00e3), de la acest tip de echilibru se calculeaz\u00e3 tensiunile la forfecare<\/p>\n<p style=\"text-align: justify;\">(\u03c4) si se compar\u00e3 cu rezistenta disponibil\u00e3\u00a0 (\u03c4<sub>f<\/sub>), , calculat\u00e3 conform criteriului de cedare Coulomb; din aceast\u00e3 comparatie ia nastere prima indicatie asupra stabilit\u00e3tii prin factorul de sigurant\u00e3<\/p>\n<p style=\"text-align: center;\"><strong>F=\u03c4<sub>f\u00a0<\/sub>\/\u03c4<\/strong><\/p>\n<p style=\"text-align: justify;\">Dintre metodele de echilibru limit\u00e3 unele iau \u00een considerare echilibrul global al corpului rigid (Culman), altele, din cauza neomogeniit\u00e3tii, divid corpul \u00een f\u00e2sii consider\u00e2nd echilibrul fiec\u00e3reia (Fellenius, Bishop, Janbu, etc).<\/p>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.geostru.eu\/wp-content\/uploads\/2016\/06\/INTRO_PENDIO.bmp\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-22672 aligncenter\" src=\"https:\/\/www.geostru.eu\/wp-content\/uploads\/2016\/06\/INTRO_PENDIO.bmp\" alt=\"INTRO_PENDIO\" width=\"636\" height=\"409\" srcset=\"https:\/\/www.geostru.eu\/wp-content\/uploads\/2016\/06\/INTRO_PENDIO.bmp 912w, https:\/\/www.geostru.eu\/wp-content\/uploads\/2016\/06\/INTRO_PENDIO-300x193.jpg 300w, https:\/\/www.geostru.eu\/wp-content\/uploads\/2016\/06\/INTRO_PENDIO-768x493.jpg 768w, https:\/\/www.geostru.eu\/wp-content\/uploads\/2016\/06\/INTRO_PENDIO-120x77.jpg 120w, https:\/\/www.geostru.eu\/wp-content\/uploads\/2016\/06\/INTRO_PENDIO-500x321.jpg 500w\" sizes=\"(max-width: 636px) 100vw, 636px\" \/><\/a><\/p>\n<p style=\"text-align: center;\"><em>R<\/em><em>eprezentarea unei sectiuni de calcul a unui taluz<\/em><\/p>\n<p style=\"text-align: justify;\">Mai jos sunt dicutate metodele echilibrului limit\u00e3 a f\u00e2siilor.<\/p>\n<h4 style=\"text-align: justify;\"><strong>Metoda f\u00e2siilor<\/strong><\/h4>\n<p>Masa supus\u00e3 alunec\u00e3rii este divizat\u00e3 \u00eentr-un num\u00e3r convenabil de f\u00e2sii. Dac\u00e3 num\u00e3rul acestora este egal cu n, problema prezint\u00e3 urm\u00e3toarele necunoscute:<\/p>\n<ul>\n<li style=\"text-align: justify;\">n valori ale fortelor normale N<sub>i<\/sub> care actioneaz\u00e3 asupra bazei fiec\u00e3rei f\u00e2sii;<\/li>\n<li style=\"text-align: justify;\">n valori ale fortelor de forfecare la baza f\u00e2siei T<sub>i<\/sub>;<a href=\"https:\/\/www.geostru.eu\/wp-content\/uploads\/2016\/06\/concio_intro_1.bmp\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-22576 size-full alignright\" src=\"https:\/\/www.geostru.eu\/wp-content\/uploads\/2016\/06\/concio_intro_1.bmp\" alt=\"concio_intro_1\" width=\"338\" height=\"333\" srcset=\"https:\/\/www.geostru.eu\/wp-content\/uploads\/2016\/06\/concio_intro_1.bmp 338w, https:\/\/www.geostru.eu\/wp-content\/uploads\/2016\/06\/concio_intro_1-80x80.jpg 80w, https:\/\/www.geostru.eu\/wp-content\/uploads\/2016\/06\/concio_intro_1-300x296.jpg 300w, https:\/\/www.geostru.eu\/wp-content\/uploads\/2016\/06\/concio_intro_1-120x118.jpg 120w\" sizes=\"(max-width: 338px) 100vw, 338px\" \/><\/a><\/li>\n<li style=\"text-align: justify;\">(n-1) forte normale E<sub>i\u00a0<\/sub>care actioneaz\u00e3 pe interfata f\u00e2siilor;<\/li>\n<li style=\"text-align: justify;\">(n-1) forte tangenziale X<sub>i<\/sub> care actioneaz\u00e3 pe interfata f\u00e2siilor<\/li>\n<li style=\"text-align: justify;\">n valori ale coordonatei \u201ca\u201d care identific\u00e3 punctul de aplicare a E<sub>i<\/sub>;<\/li>\n<li style=\"text-align: justify;\">(n-1) valori ale coordonatei care identific\u00e3 punctul de aplicare a X<sub>i<\/sub>;<\/li>\n<li style=\"text-align: justify;\">necunoscut\u00e3 constituit\u00e3 din factorul de sigurant\u00e3 F.<\/li>\n<\/ul>\n<p style=\"text-align: justify;\">\u00cen total sunt (6n-2) necunoscute.<\/p>\n<p style=\"text-align: justify;\">\u00een timp ce ecuatiile disponibile sunt:<\/p>\n<ul style=\"text-align: justify;\">\n<li>ecuatii de echilibru ale momentelor n;<\/li>\n<li>ecuatii de echilibru la deplasare vertical\u00e3 n;<\/li>\n<li>ecuatii de echilibru la deplasare orizontal\u00e3 n;<\/li>\n<li>ecuatii care se refer\u00e3 la criteriul de cedare n.<\/li>\n<\/ul>\n<p style=\"text-align: justify;\">Num\u00e3rul total de ecuatii 4n<\/p>\n<p style=\"text-align: justify;\">Problema este static nedeterminat\u00e3 iar gradul de nedeterminare este de:<\/p>\n<p style=\"text-align: center;\">i=(6n-2)-4n=2n-2<\/p>\n<p style=\"text-align: justify;\">Gradul de nedeterminare se reduce ulterior cu (n-2) \u00eentruc\u00e2t se presupune c\u00e3:<br \/>\nNi este aplicat \u00een punctul mediu al f\u00e2siei, echivalent cu a presupune c\u00e3 tensiunile normale totale sunt uniform distribuite.<br \/>\nDiversele metode care se bazeaz\u00e3 pe teoria echilibrului limit\u00e3 se diferentiaz\u00e3 prin modul \u00een care se elimin\u00e3 (n-2) nedeterminate.<\/p>\n<h4 style=\"text-align: justify;\"><strong>\u00a0Metoda\u00a0<a href=\"https:\/\/en.wikipedia.org\/wiki\/Slope_stability_analysis\">Fellenius<\/a>\u00a0(1927)<\/strong><\/h4>\n<p>Cu aceast\u00e3 metod\u00e3 (valid\u00e3 numai pentru suprafete de alunecare de form\u00e3 circular\u00e3) nu se iau \u00een considerare fortele dintre f\u00e2sii astfel \u00eenc\u00e2t necunoscutele se reduc la:<br \/>\n<a href=\"https:\/\/www.geostru.eu\/wp-content\/uploads\/2016\/06\/ConcioIntro.zoom17.png.bmp\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-22580 size-full alignright\" src=\"https:\/\/www.geostru.eu\/wp-content\/uploads\/2016\/06\/ConcioIntro.zoom17.png.bmp\" alt=\"ConcioIntro.zoom17.png\" width=\"361\" height=\"424\" srcset=\"https:\/\/www.geostru.eu\/wp-content\/uploads\/2016\/06\/ConcioIntro.zoom17.png.bmp 361w, https:\/\/www.geostru.eu\/wp-content\/uploads\/2016\/06\/ConcioIntro.zoom17.png-255x300.jpg 255w, https:\/\/www.geostru.eu\/wp-content\/uploads\/2016\/06\/ConcioIntro.zoom17.png-120x141.jpg 120w\" sizes=\"(max-width: 361px) 100vw, 361px\" \/><\/a><\/p>\n<ul>\n<li>n valori ale fortelor normale N<sub>i<\/sub>;<\/li>\n<li>n valori ale fortelor de forfecare T<sub>i<\/sub>;<\/li>\n<li>1 factor de sigurant\u00e3.<\/li>\n<\/ul>\n<p>Necunoscutele (2n+1). Ecuatiile disponibile sunt:<\/p>\n<ul>\n<li>n ecuatii de echilibru la deplasare vertical\u00e3;<\/li>\n<li>n ecuatii care se refer\u00e3 la criteriul de cedare;<\/li>\n<li>1 ecuatie de echilibru a momentelor globale.<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<p style=\"text-align: center;\">F={\u03a3<sub>\u00ec<\/sub>[c<sub>i<\/sub>\u00b7l<sub>i<\/sub>+(W<sub>i<\/sub>\u00b7cos\u03b1<sub>i<\/sub>-u<sub>i<\/sub>\u00b7l<sub>i<\/sub>)\u00b7tan\u03c6<sub>i<\/sub>}\/(\u03a3<sub>\u00ec<\/sub>\u00b7sin\u03b1<sub>i<\/sub>)<\/p>\n<p>Aceast\u00e3 ecuatie este simplu de rezolvat dar s-a observat c\u00e3 ofera rezultate conservatoare (factori de sigurant\u00e3 mici), mai ales pentru suprafetele ad\u00e2nci sau la cresterea presiunii neutrale.<\/p>\n<h4>Metoda <a href=\"https:\/\/en.wikipedia.org\/wiki\/Bishop\">Bishop <\/a>(1955)<\/h4>\n<p>Cu aceast\u00e3 metod\u00e3 nu se neglijeaz\u00e3 niciun efect al fortelor ce actioneaz\u00e3 asupra blocurilor, fiind prima metod\u00e3 ce descrie problemele legate de metodele traditionale.<br \/>\nEcuatiile utilizate pentru rezolvarea problemei sunt:<\/p>\n<p><strong>\u03a3 F<sub>y<\/sub>=0 \u00a0\u03a3 M<sub>0<\/sub>=0 Criteriu de cedare.<\/strong><\/p>\n<p style=\"text-align: center;\"><a href=\"https:\/\/www.geostru.eu\/wp-content\/uploads\/2016\/06\/concio_bishop_sempl.zoom17.png.bmp\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-22584 size-full aligncenter\" src=\"https:\/\/www.geostru.eu\/wp-content\/uploads\/2016\/06\/concio_bishop_sempl.zoom17.png.bmp\" alt=\"concio_bishop_sempl.zoom17.png\" width=\"339\" height=\"366\" srcset=\"https:\/\/www.geostru.eu\/wp-content\/uploads\/2016\/06\/concio_bishop_sempl.zoom17.png.bmp 339w, https:\/\/www.geostru.eu\/wp-content\/uploads\/2016\/06\/concio_bishop_sempl.zoom17.png-278x300.jpg 278w, https:\/\/www.geostru.eu\/wp-content\/uploads\/2016\/06\/concio_bishop_sempl.zoom17.png-120x130.jpg 120w\" sizes=\"(max-width: 339px) 100vw, 339px\" \/><\/a>F={\u03a3<sub>\u00ec<\/sub>[c<sub>i<\/sub>\u00b7b<sub>i<\/sub>+(W<sub>i<\/sub>-u<sub>i<\/sub>\u00b7b<sub>i<\/sub>+\u0394X<sub>i<\/sub>)\u00b7tan\u03c6<sub>i<\/sub>]\u00b7[sec\u03b1<sub>i<\/sub>\/(1+tan\u03b1<sub>i<\/sub>\u00b7tan\u03c6<sub>i<\/sub>\/F)]}\/(\u03a3<sub>\u00ec<\/sub>W<sub>i\u00b7<\/sub>sin\u03b1<sub>i<\/sub>)<\/p>\n<p style=\"text-align: justify;\">Valoriale lui F si\u00a0\u0394X pentru fiecare element care satisface aceasta ecuatie dau o solutie riguroas\u00e3 problemei. Ca si prim\u00e3 aproximare se ia \u0394X = 0 si se itereaz\u00e3 pentru calculul factorului de sigurant\u00e3, acest procedeu fiind cunoscut ca si metoda Bishop obisnuit\u00e3, erorile comise fat\u00e3 de metoda complet\u00e3 sunt de circa 1 %.<\/p>\n<h4>Metoda <a href=\"https:\/\/en.wikipedia.org\/wiki\/Slope_stability_analysis\">Janbu<\/a>\u00a0 (1967)<\/h4>\n<p style=\"text-align: justify;\">Janbu a extins metoda lui Bishop la suprafetele de alunecare de form\u00e3 generic\u00e3. C\u00e2nd sunt tratate suprafetele de alunecare de form\u00e3 generic\u00e3 bratul fortelor se schimb\u00e3 (\u00een cazul suprafetelor circulare r\u00e3m\u00e2ne constant si egal cu raza) &#8211; de aceea este mai convenabil\u00e3 calcularea ecuatiei momentului fat\u00e3 de marginea inferioar\u00e3 a fiec\u00e3rei f\u00e2sii.<\/p>\n<p style=\"text-align: center;\">F={\u03a3<sub>\u00ec<\/sub>[c<sub>i<\/sub>\u00b7b<sub>i<\/sub>+(W<sub>i<\/sub>-u<sub>i<\/sub>\u00b7b<sub>i<\/sub>+\u0394X<sub>i<\/sub>)\u00b7tan\u03c6<sub>i<\/sub>]\u00b7[sec^(2)\u03b1<sub>i<\/sub>\/(1+tan\u03b1<sub>i<\/sub>\u00b7tan\u03c6<sub>i<\/sub>\/F)]}\/(\u03a3<sub>\u00ec<\/sub>W<sub>i\u00b7<\/sub>tan\u03b1<sub>i<\/sub>)<\/p>\n<p style=\"text-align: center;\"><a href=\"https:\/\/www.geostru.eu\/wp-content\/uploads\/2016\/06\/Jambu1.zoom17.png.bmp\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-22588 size-full\" src=\"https:\/\/www.geostru.eu\/wp-content\/uploads\/2016\/06\/Jambu1.zoom17.png.bmp\" alt=\"Jambu1.zoom17.png\" width=\"392\" height=\"355\" srcset=\"https:\/\/www.geostru.eu\/wp-content\/uploads\/2016\/06\/Jambu1.zoom17.png.bmp 392w, https:\/\/www.geostru.eu\/wp-content\/uploads\/2016\/06\/Jambu1.zoom17.png-300x272.jpg 300w, https:\/\/www.geostru.eu\/wp-content\/uploads\/2016\/06\/Jambu1.zoom17.png-120x109.jpg 120w\" sizes=\"(max-width: 392px) 100vw, 392px\" \/><\/a><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-133993 \" src=\"https:\/\/www.geostru.eu\/wp-content\/uploads\/2016\/06\/Jambu2.zoom18.jpg\" alt=\"Jambu2.zoom18\" width=\"582\" height=\"403\" srcset=\"https:\/\/www.geostru.eu\/wp-content\/uploads\/2016\/06\/Jambu2.zoom18.jpg 752w, https:\/\/www.geostru.eu\/wp-content\/uploads\/2016\/06\/Jambu2.zoom18-300x208.jpg 300w, https:\/\/www.geostru.eu\/wp-content\/uploads\/2016\/06\/Jambu2.zoom18-500x346.jpg 500w\" sizes=\"(max-width: 582px) 100vw, 582px\" \/><\/p>\n<p style=\"text-align: center;\">Actiuni pe f\u00e2sia i conform teoriei lui Jambu si reprezentarea f\u00e2siei<\/p>\n<p style=\"text-align: justify;\">Presupun\u00e2nd c\u00e3\u00a0\u0394X<sub>i <\/sub>= 0 se obtine metoda obisnuit\u00e3.\u00a0Janbu a mai propus si o metod\u00e3 pentru corectarea factorului de sigurant\u00e3 obtinut cu metoda obisnuit\u00e3:<\/p>\n<p style=\"text-align: center;\">F<sub>cor<\/sub>=f<sub>0<\/sub>\u00b7F<\/p>\n<p style=\"text-align: justify;\">unde f<sub>0 <\/sub> apare pe grafic \u00een functie de geometrie si de parametrii geotehnici.Aceast\u00e3 corectie este indicat\u00e3 pentru taluzurile putin \u00eenclinate.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-133997 size-medium aligncenter\" src=\"https:\/\/www.geostru.eu\/wp-content\/uploads\/2016\/06\/Jambu4.zoom17-300x117.jpg\" alt=\"\" width=\"300\" height=\"117\" srcset=\"https:\/\/www.geostru.eu\/wp-content\/uploads\/2016\/06\/Jambu4.zoom17-300x117.jpg 300w, https:\/\/www.geostru.eu\/wp-content\/uploads\/2016\/06\/Jambu4.zoom17-768x299.jpg 768w, https:\/\/www.geostru.eu\/wp-content\/uploads\/2016\/06\/Jambu4.zoom17-500x195.jpg 500w, https:\/\/www.geostru.eu\/wp-content\/uploads\/2016\/06\/Jambu4.zoom17.jpg 857w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-134001 size-medium aligncenter\" src=\"https:\/\/www.geostru.eu\/wp-content\/uploads\/2016\/06\/Jambu3.zoom17-300x232.jpg\" alt=\"\" width=\"300\" height=\"232\" srcset=\"https:\/\/www.geostru.eu\/wp-content\/uploads\/2016\/06\/Jambu3.zoom17-300x232.jpg 300w, https:\/\/www.geostru.eu\/wp-content\/uploads\/2016\/06\/Jambu3.zoom17-500x387.jpg 500w, https:\/\/www.geostru.eu\/wp-content\/uploads\/2016\/06\/Jambu3.zoom17.jpg 608w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<h4>Metoda Bell (1968)<\/h4>\n<p style=\"text-align: justify;\">Fortele ce actioneaz\u00e3 pe corpurile \u00een alunecare includ greutatea efectiv\u00e3 a terenului, W, fortele seismice pseudostatice orizontale si verticale K<sub>x<\/sub>\u00b7W si K<sub>y<\/sub>\u00b7W, fortele orizontale si verticale X si Z aplicate extern asupra profilului taluzului si rezultanta eforturilor totale normale de forfecare\u00a0\u03c3 si\u00a0\u03c4 ce actioneaz\u00e3 pe suprafata potential\u00e3 de alunecare.\u00a0Efortul total normal poate include un exces de presiune \u00een pori u care trebuie s\u00e3 fie specificat\u00e3 la introducerea parametrilor de fort\u00e3 efectiv\u00e3.<br \/>\nPractic aceast\u00e3 metod\u00e3 poate fi considerat\u00e3 o extensie a metodei cercului de frecare pentru sectiuni omogene descrise anterior de c\u00e3tre Taylor.<br \/>\nConform legii de rezistent\u00e3 Mohr-Coulomb \u00een termeni de tensiune efectiv\u00e3, forta de forfecare ce actioneaz\u00e3 aspra bazei f\u00e2siei este dat\u00e3 de:<\/p>\n<p><a href=\"https:\/\/www.geostru.eu\/wp-content\/uploads\/2016\/06\/Bell.zoom25.png.bmp\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-22604 size-full aligncenter\" src=\"https:\/\/www.geostru.eu\/wp-content\/uploads\/2016\/06\/Bell.zoom25.png.bmp\" alt=\"Bell.zoom25.png\" width=\"541\" height=\"416\" srcset=\"https:\/\/www.geostru.eu\/wp-content\/uploads\/2016\/06\/Bell.zoom25.png.bmp 541w, https:\/\/www.geostru.eu\/wp-content\/uploads\/2016\/06\/Bell.zoom25.png-300x231.jpg 300w, https:\/\/www.geostru.eu\/wp-content\/uploads\/2016\/06\/Bell.zoom25.png-120x92.jpg 120w, https:\/\/www.geostru.eu\/wp-content\/uploads\/2016\/06\/Bell.zoom25.png-500x384.jpg 500w\" sizes=\"(max-width: 541px) 100vw, 541px\" \/><\/a><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: center;\">T<sub>i<\/sub>=[c<sub>i<\/sub>\u00b7L<sub>i<\/sub>+(N<sub>i<\/sub>-u<sub>ci<\/sub>\u00b7L<sub>i<\/sub>)\u00b7tan\u03c6<sub>i<\/sub>]\/F<\/p>\n<p>\u00een care:<\/p>\n<p><strong>F<\/strong> = factorul de sigurant\u00e3;<br \/>\n<strong>c<sub>i<\/sub><\/strong> = coeziunea efectiv\u00e3 (sau total\u00e3) la baza f\u00e2siei i;<br \/>\n<strong>\u03c6<sub>i<\/sub><\/strong> \u00a0= unghiul de frecare efectiv (= 0 cu coeziune total\u00e3) la baza f\u00e2siei;<br \/>\n<strong>L<sub>i<\/sub><\/strong> \u00a0= lungimea bazei f\u00e2siei i;<br \/>\n<strong>u<sub>ci<\/sub><\/strong> \u00a0= presiunea \u00een porii \u00een centrul bazei f\u00e2siei i.<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify;\">Echilibrul se obtine egal\u00e2nd cu zero suma fortelor orizontale, suma fortelor verticale si suma momentelor fat\u00e3 de origine.\u00a0Este adoptat\u00e3 urm\u00e3toarea presupunere aspra variatiei tensiunii normale ce actioneaz\u00e3 pe suprafata potential\u00e3 de alunecare:<\/p>\n<p style=\"text-align: center;\">\u03c3<sub>ci=[C<sub>1<\/sub>\u00b7(1-K<sub>z<\/sub>)\u00b7(W<sub>i<\/sub>\u00b7cos\u03b1<sub>i<\/sub>)\/L<sub>i<\/sub>]+C<sub>2<\/sub>\u00b7f(x<sub>ci<\/sub>,y<sub>ci<\/sub>,z<sub>ci<\/sub>)<\/sub><\/p>\n<p>\u00een care primul termen al ecuatiei include expresia:<\/p>\n<p>W<sub>i<\/sub>\u00b7cos\u03b1<sub>i<\/sub>\/L<sub>i<\/sub>= valoarea efortului normal total cu metoda obisnuit\u00e3 a f\u00e2siei.<\/p>\n<p>Cel de-al doilea termen al ecuatiei include functia:<\/p>\n<p style=\"text-align: center;\">f=sin2\u03c0\u00b7[(x<sub>n<\/sub>-x<sub>ci<\/sub>)\/(x<sub>n<\/sub>-x<sub>0<\/sub>)]<\/p>\n<p style=\"text-align: justify;\">Unde <strong>x<sub>0<\/sub><\/strong>\u00a0si <strong>x<sub>n<\/sub><\/strong>\u00a0sunt abscisele primului si ultimului punct ale suprafetei de alunecare, \u00een timp ce <strong>x<sub>ci<\/sub><\/strong> reprezint\u00e3 abscisa punctului mediu al bazei f\u00e2siei i. O parte sensibil\u00e3 la reducerea greut\u00e3tii asociat\u00e3 cu o acceleratie vertical\u00e3 a terenului K<sub>z<\/sub> g g poate fi transmis\u00e3 direct bazei si este inclus\u00e3 \u00een factorul (1 &#8211; K<sub>z<\/sub>). Efortul normal total la baza unei f\u00e2sii este dat de::<\/p>\n<p style=\"text-align: center;\">N<sub>i<\/sub>= \u03c3<sub>ci<\/sub>\u00a0\u00b7L<sub>i<\/sub><\/p>\n<p style=\"text-align: justify;\">Solutia ecuatiilor de echilibru se afl\u00e3 rezolv\u00e2nd un sistem liniar de trei ecuatii obtinute multiplic\u00e2nd ecuatiile de echilibru cu factorul de sigurant\u00e3 F , \u00eenlocuind expresia lui N<sub>i<\/sub>\u00a0 si \u00eenmultind fiecare termen al coeziunii cu un coeficient arbitrar C<sub>3<\/sub>.<\/p>\n<p style=\"text-align: justify;\"><strong>Metoda\u00a0\u00a0<a href=\"https:\/\/www.researchgate.net\/profile\/Sarada_Sarma\/publication\/267637426_Stability_Analysis_of_Embankments_and_Slopes\/links\/545641f70cf2cf5164802dca.pdf\">Sarma <\/a>\u00a0(1973)<br \/>\n<\/strong>Metoda Sarma este o metod\u00e3 simpl\u00e3 dar precis\u00e3 pentru analiza stabilit\u00e3tii taluzurilor, ce permite determinarea acceleratiei seismice orizontale cerute p\u00e2n\u00e3 \u00een momentul \u00een care terenul, delimitat de suprafata de alunecare si de profilul topografic, atinge starea de echilibru limit\u00e3 (acceleratie critic\u00e3 K<sub>c<\/sub>) si, \u00een acelasi timp, permite calcularea factorului de sigurant\u00e3 obtinut la fel ca si pentru celelalte metode comune din geotehnic\u00e3.<br \/>\nEste o metod\u00e3 bazat\u00e3 pe principiul echilibrului limit\u00e3 si al f\u00e2siilor. Este considerat echilibrul unei mase de teren \u00een alunecare \u00eemp\u00e3rtit\u00e3 \u00een n f\u00e2sii verticale de grosime suficient de mic\u00e3 pentru a considera admisiblil\u00e3 presupunerea c\u00e3 efortul normal Ni actioneaz\u00e3 \u00een punctul mediu al bazei f\u00e2siei.<\/p>\n<p style=\"text-align: justify;\">Ecuatiile de luat \u00een considerare sunt:<\/p>\n<ul>\n<li>Ecuatia echilibrului la deplasarea orizontal\u00e3 a f\u00e2siei;<\/li>\n<li>Ecuatia echilibrului la deplasarea vertical\u00e3 a f\u00e2siei;<\/li>\n<li>Ecuatia echilibrului momentelor.<\/li>\n<\/ul>\n<p>Conditii de echilibru la deplasarea orizontal\u00e3 si vertical\u00e3:<\/p>\n<p style=\"text-align: center;\">N<sub>i<\/sub>\u00b7cos\u03b1<sub>i<\/sub>+T<sub>i<\/sub>\u00b7sin\u03b1<sub>i<\/sub>=W<sub>i<\/sub>-\u0394X<sub>i<\/sub><br \/>\nT<sub>i<\/sub>\u00b7cos\u03b1<sub>i<\/sub>-N<sub>i<\/sub>\u00b7sin\u03b1<sub>i<\/sub>=KW<sub>i<\/sub>-\u0394E<sub>i<\/sub><\/p>\n<p>Se presupune c\u00e3 \u00een absenta fortelor externe pe suprafata liber\u00e3 avem:<\/p>\n<p style=\"text-align: center;\">\u03a3 \u0394E<sub>i<\/sub> = 0<br \/>\n\u03a3 \u0394X<sub>\u00ec<\/sub>\u00a0 = 0<\/p>\n<p style=\"text-align: justify;\">Unde E<sub>i<\/sub>\u00a0si X<sub>i<\/sub> reprezint\u00e3 fortele orizzontale si respectiv verticale pe fata i a f\u00e2siei generice i. Ecuatia echilibrului momentelor este scris\u00e3 aleg\u00e2nd ca si punct de referint\u00e3 baricentrul \u00eentregului corp; astfel, dup\u00e3 ce s-au parcurs o serie de pozitii si transform\u00e3ri trigonometrice si algebrice, \u00een <strong>metoda Sarma<\/strong> solutia problemei vine din rezolvarea a dou\u00e3 ecuatii:<\/p>\n<p style=\"text-align: center;\"><a href=\"https:\/\/www.geostru.eu\/wp-content\/uploads\/2016\/06\/sarma2.zoom30.png.bmp\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-22608 size-full\" src=\"https:\/\/www.geostru.eu\/wp-content\/uploads\/2016\/06\/sarma2.zoom30.png.bmp\" alt=\"sarma2.zoom30.png\" width=\"650\" height=\"391\" srcset=\"https:\/\/www.geostru.eu\/wp-content\/uploads\/2016\/06\/sarma2.zoom30.png.bmp 650w, https:\/\/www.geostru.eu\/wp-content\/uploads\/2016\/06\/sarma2.zoom30.png-300x180.jpg 300w, https:\/\/www.geostru.eu\/wp-content\/uploads\/2016\/06\/sarma2.zoom30.png-120x72.jpg 120w, https:\/\/www.geostru.eu\/wp-content\/uploads\/2016\/06\/sarma2.zoom30.png-500x301.jpg 500w\" sizes=\"(max-width: 650px) 100vw, 650px\" \/><\/a><\/p>\n<p style=\"text-align: center;\">Actiuni pe f\u00e2sia i conform teoriei lui Sarma<\/p>\n<p style=\"text-align: center;\">\u03a3 \u0394X<sub>\u00ec<\/sub>\u00b7tan(\u03c8<sub>i<\/sub>&#8211; \u03b1<sub>i<\/sub>)+\u03a3 \u0394E<sub>i<\/sub>=\u03a3 \u0394<sub>i<\/sub>-KW<sub>i<\/sub><\/p>\n<p style=\"text-align: center;\">\u03a3 \u0394X<sub>\u00ec<\/sub>\u00b7[(y<sub>mi<\/sub>-y<sub>G<\/sub>)\u00b7tan(\u03c8<sub>i<\/sub>&#8211; \u03b1<sub>i<\/sub>)+(x<sub>mi<\/sub>-x<sub>G<\/sub>)]=\u03a3 W<sub>\u00ec<\/sub>\u00a0\u00b7(x<sub>mi<\/sub>-x<sub>G<\/sub>)+\u03a3 \u0394<sub>i<\/sub>-(y<sub>mi<\/sub>-y<sub>G<\/sub>)<\/p>\n<p style=\"text-align: justify;\">Rezolvarea impune g\u00e3sirea valorii <strong>K<\/strong> (acceleratie seismic\u00e3) corespunz\u00e3toare unui anumit factor de sigurant\u00e3; si \u00een special, g\u00e3sirea valorii acceleratiei <strong>K<\/strong> ce corespunde factorului de sigurant\u00e3 F = 1 , sau acceleratia critic\u00e3.<br \/>\nAvem:<\/p>\n<p>K=Kc \u00a0 \u00a0 <strong>acceleratia critic\u00e3 dac\u00e3\u00a0<\/strong>\u00a0F=1<br \/>\nF=Fs \u00a0 \u00a0 <strong>factorul de sigurant\u00e3 \u00een conditii statice dac\u00e3<\/strong>\u00a0<strong>\u00a0<\/strong>K=0<\/p>\n<p style=\"text-align: justify;\">Cea de-a doua parte a problemei metodei Sarma const\u00e3 \u00een g\u00e3sirea unei distributii de forfe interne \u00a0X<sub>i<\/sub>\u00a0si E<sub>i<\/sub> astfel \u00eenc\u00e2t s\u00e3 verifice echilibrul f\u00e2siei si cel global al \u00eentregului corp, f\u00e3r\u00e3 \u00eenc\u00e3lcarea criteriului de cedare.<br \/>\nS-a constatat c\u00e3 o solutie acceptabil\u00e3 a problemei se poate obtine lu\u00e2nd \u00een calcul urmatoarea distributie pentru fortele X<sub>i\u00a0<\/sub>\u00a0:<\/p>\n<p style=\"text-align: center;\">\u03a3\u0394X<sub>\u00ec<\/sub>=\u03bb\u00b7\u0394Q<sub>\u00ec<\/sub>=\u03bb\u00b7(Q<sub>\u00ec+1<\/sub>-Q<sub>1<\/sub>)<\/p>\n<p style=\"text-align: justify;\">unde Q<sub>i<\/sub> este o functie cunoscut\u00e3, \u00een care se iau \u00een considerare parametrii geotehnici medii pe fata i a f\u00e2siei i, iar l reprezint\u00e3 o necunoscut\u00e3. Solutia complet\u00e3 a problemi se obtine cu ajutorul valorilor\u00a0K<sub>c<\/sub>, l si\u00a0F, care permit si obtinerea distributiei fortelor dintre f\u00e2sii.<\/p>\n<p style=\"text-align: justify;\"><strong>Metoda Spencer \u00a0 (1967)<br \/>\n<\/strong>Metoda este bazat\u00e3 pe presupunerile:<\/p>\n<ol style=\"text-align: justify;\">\n<li>Fortele de interfat\u00e3 de-a lungul suprafetelor de divizare ale f\u00e2siei sunt orientate paralel \u00eentre ele si \u00eenclinate fat\u00e3 de orizontal\u00e3 cu un unghi \u03b8;<\/li>\n<li>Toate momentele sunt nule Mi =0 \u00a0i=1\u2026..n<\/li>\n<\/ol>\n<p style=\"text-align: justify;\">Metoda satisface toate ecuatiile de static\u00e3 si este echivalent\u00e3 cu metoda <strong>Morgenstern si Price<\/strong> c\u00e2nd functia f(x) = 1\u00a0. Impun\u00e2nd echilibrul momentelor fat\u00e3 de centrul arcului descris al suprafetei de alunecare avem:<\/p>\n<p>1)\u00a0\u03a3Q<sub>\u00ec<\/sub>\u00b7R\u00b7cos(\u03b1-\u03b8)=0<\/p>\n<p>unde:<br \/>\n<a href=\"https:\/\/www.geostru.eu\/wp-content\/uploads\/2016\/06\/spencer.bmp\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-22612 size-full alignright\" src=\"https:\/\/www.geostru.eu\/wp-content\/uploads\/2016\/06\/spencer.bmp\" alt=\"spencer\" width=\"383\" height=\"508\" srcset=\"https:\/\/www.geostru.eu\/wp-content\/uploads\/2016\/06\/spencer.bmp 383w, https:\/\/www.geostru.eu\/wp-content\/uploads\/2016\/06\/spencer-226x300.jpg 226w, https:\/\/www.geostru.eu\/wp-content\/uploads\/2016\/06\/spencer-120x159.jpg 120w\" sizes=\"(max-width: 383px) 100vw, 383px\" \/><\/a><\/p>\n<p>Q<sub>\u00ec<\/sub>=0<\/p>\n<p>forta de interactiune dintre f\u00e2sii;<\/p>\n<p><strong>R<\/strong> = raza arcului cercului;<br \/>\n<strong>\u03b8<\/strong> = unghiul de \u00eenclinatie a fortei Q<sub>i<\/sub> fat\u00e3 de orizontal\u00e3.<\/p>\n<p>Impun\u00e2nd echilibrul fortelor orizontale si verticale avem:<\/p>\n<p style=\"text-align: center;\">\u03a3(Q<sub>\u00ec<\/sub>\u00b7cos\u03b8)=0<br \/>\n\u03a3(Q<sub>\u00ec<\/sub>\u00b7sen\u03b8)=0<\/p>\n<p>Presupun\u00e2nd c\u00e3 fortele Q<sub>i<\/sub>\u00a0 sunt paralele \u00eentre ele, se poate scrie si:<\/p>\n<p>2) \u03a3Q<sub>\u00ec<\/sub>=0<\/p>\n<p style=\"text-align: center;\">Q<sub>\u00ec<\/sub>={c\/F<sub>s<\/sub>\u00b7(W\u00b7cos\u03b1-\u03b3<sub>w<\/sub>\u00b7h\u00b7l\u00b7sec\u03b1)\u00b7tan\u03b1\/F<sub>s<\/sub>-W\u00b7sin\u03b1}\/{cos(\u03b1-\u03b8)\u00b7[(F<sub>s<\/sub>+tan\u03c6\u00b7tan(\u03b1-\u03b8)]\/F<sub>s<\/sub>}<\/p>\n<p>Metoda propune calcularea a doi coeficienti de sigurant\u00e3: primul (F<sub>sm<\/sub>) obinut din 1), legat de echilibrul momentelor; cel de-al doilea (F<sub>sf<\/sub>) din 2) legat de echilibrul fortelor. \u00cen pratic\u00e3 se rezolv\u00e3 1) si 2) pentru un interval dat de valori ale unghiului \u03b8, consider\u00e2nd ca valoare unic\u00e3 a coeficientului de sigurant\u00e3 aceea pentru care:<\/p>\n<p style=\"text-align: center;\">F<sub>sm<\/sub>=F<sub>sf<\/sub><\/p>\n<p style=\"text-align: justify;\"><strong>Metoda \u00a0 Morgenstern si\u00a0Price (1965)<br \/>\n<\/strong>Se stabileste o relatie \u00eentre componentele fortelor de interfat\u00e3 de tipul X = \u03bb f(x)E, unde \u03bb este un factor de scar\u00e3 si f(x), functie de pozitiile lui E si lui X, defineste o relatie \u00eentre variatia fortei X si a fortei E \u00een interiorul masei ce alunec\u00e3. Functia f(x) este aleas\u00e3 \u00een mod arbitrar (constant\u00e3, sinusoidal\u00e3, semisinusoidal\u00e3, trapezoidal\u00e3, etc.) si infuenteaz\u00e3 putin rezultatul, dar trebuie verificat ca valorile rezultate pentru necunoscute s\u00e3 fie acceptabile.\u00a0Particularitatea acestei metode este c\u00e3 masa este subdivizat\u00e3 \u00een f\u00e2sii infinitezimale la care se impun ecuatiile de echilibru la deplasarea orizontal\u00e3 si vertical\u00e3 si de cedare pe baza f\u00e2siilor. \u00a0Se ajunge la o prim\u00e3 ecuatie diferential\u00e3 care leg\u00e3 fortele de interfat\u00e3 necunoscute E, X, coeficientul de sigurant\u00e3 Fs, greutatea f\u00e2siei infinitezimale dW si rezultanta presiunilor neutrale la baz\u00e3 dU.<\/p>\n<p>Se obtine asa-numita <strong>\u201cecuatie a fortelor\u201d<\/strong>:<\/p>\n<p style=\"text-align: center;\">c&#8217;\u00b7(\u03b1\/F<sub>s<\/sub>)+tan\u03c6&#8217;\u00b7[(dW\/dx)-(dX\/dx)-tan\u03b1(dE\/dx)-sec\u03b1\u00b7(dU\/dx)]=(dE\/dx)-tan\u03b1\u00b7[(dX\/dx)-(dW\/dx)]<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-134005 size-full\" src=\"https:\/\/www.geostru.eu\/wp-content\/uploads\/2016\/06\/mep-1.jpg\" alt=\"mep\" width=\"873\" height=\"431\" srcset=\"https:\/\/www.geostru.eu\/wp-content\/uploads\/2016\/06\/mep-1.jpg 873w, https:\/\/www.geostru.eu\/wp-content\/uploads\/2016\/06\/mep-1-300x148.jpg 300w, https:\/\/www.geostru.eu\/wp-content\/uploads\/2016\/06\/mep-1-768x379.jpg 768w, https:\/\/www.geostru.eu\/wp-content\/uploads\/2016\/06\/mep-1-500x247.jpg 500w\" sizes=\"(max-width: 873px) 100vw, 873px\" \/><\/p>\n<p style=\"text-align: center;\">Actiuni pe f\u00e2sia i conform teoriilor Mongester si Price si reprezentarea ansamblului<\/p>\n<p style=\"text-align: justify;\">O a doua ecuatie, numit\u00e3 si <strong>\u201cecuatia momentelor\u201d<\/strong>, este scris\u00e3 impun\u00e2nd conditia de echilibru la rotatie fat\u00e3 de centrul bazei::<\/p>\n<p style=\"text-align: center;\">X=d(E<sub>\u03b3<\/sub>)\/dx-\u03b3\u00b7dE\/dx<\/p>\n<p style=\"text-align: justify;\">Aceste dou\u00e3 ecuatii sunt extinse pentru integrarea la \u00eentreaga mas\u00e3 a alunecarii.\u00a0Metoda de calcul satisface toate ecuatiile de echilibru si se poate aplica suprafetelor de orice form\u00e3, dar implic\u00e3 \u00een mod necesar folosirea unui calculator.<\/p>\n<p style=\"text-align: justify;\"><strong>Metoda <a href=\"http:\/\/download.geostru.eu\/documents\/Zeng Liang.pdf\">Zeng e Liang<\/a> (2002)<br \/>\n<\/strong>Zeng si Liang au efectuat o serie de analize parametrice pe un model bidimensional dezvoltat cu un cod \u00een elemente finite, ce reproduce cazul pilotilor imersi \u00eentr-un teren \u00een miscare (drilled shafts). Modelul bidimensional reproduce o f\u00e2sie de teren de grosime unitar\u00e3 si presupune c\u00e3 fenomenul survine \u00een conditii de deformare plan\u00e3 \u00een directe paralel\u00e3 cu axa pilotilor. Modelul a fost utilizat pentru a cerceta influenta \u00een formarea efectului arc a anumitor parametrii ca interax \u00eentre piloti, diametrul si forma pilotilor si propriet\u00e3tile mecanice ale terenului. Autorii identific\u00e3 \u00een raportul dintre interax si diametrul pilotilor (s\/d) parametru adimensional determinant pentru formarea efectului arc.<br \/>\nProblema este static nedeterminat\u00e3, cu grad de nedeterminare egal cu (8n-4), dar cu toate acestea se poate obtine o solutie reduc\u00e2nd num\u00e3rul necunoscutelor si consider\u00e2nd deci ipoteze simplificative, astfel \u00eenc\u00e2t s\u00e3 fac\u00e3 problema determinat\u00e3.<\/p>\n<p>Presupunerile care fac problema determinat\u00e3 sunt:<br \/>\n<a href=\"https:\/\/www.geostru.eu\/wp-content\/uploads\/2016\/06\/concio_zeng_Liang.zoom20.png.bmp\"><img loading=\"lazy\" decoding=\"async\" class=\"alignright wp-image-22620 size-full\" src=\"https:\/\/www.geostru.eu\/wp-content\/uploads\/2016\/06\/concio_zeng_Liang.zoom20.png.bmp\" alt=\"concio_zeng_Liang.zoom20.png\" width=\"342\" height=\"516\" srcset=\"https:\/\/www.geostru.eu\/wp-content\/uploads\/2016\/06\/concio_zeng_Liang.zoom20.png.bmp 342w, https:\/\/www.geostru.eu\/wp-content\/uploads\/2016\/06\/concio_zeng_Liang.zoom20.png-199x300.jpg 199w, https:\/\/www.geostru.eu\/wp-content\/uploads\/2016\/06\/concio_zeng_Liang.zoom20.png-120x181.jpg 120w\" sizes=\"(max-width: 342px) 100vw, 342px\" \/><\/a><\/p>\n<p>-K<sub>y<\/sub> sunt luate ca orizontale pentru a reduce num\u00e3rul total de necunoscute cu (n-1) la (7n-3)<br \/>\n-Fortele normale la baza f\u00e2siei actioneaz\u00e3 \u00een punctul mediu, reduc\u00e2nd necunoscutele cu n la (6n-3)<br \/>\n-Pozitia \u00eempingerilor laterale si la o treime din \u00een\u00e3ltimea medie a distantei dintre f\u00e2sii reduce necunosctutele cu (n-1) la (5n-2)<br \/>\n-Fortele (Pi-1) si Pi se iau paralele la \u00eenclinatia bazei f\u00e2siei (\u03b1i), reduc\u00e2nd num\u00e3rul necunoscutelor cu (n-1) la (4n-1)<br \/>\n-Se ia o singur\u00e3 constant\u00e3 de curgere pentru toate f\u00e2siile, reduc\u00e2nd necunoscutele cu (n) la (3n-1)<\/p>\n<p>Num\u00e3rul total de necunoscute este redus astfel la (3n), de calculat folosind factorul de transfer de sarcin\u00e3. Se tine cont de faptul c\u00e3 forta de stabilizare transmis\u00e3 pe teren aval de piloti este redus\u00e3 cu o cantitate R, numit\u00e3 factor de reducere, ce se calculeaz\u00e3 ca:<\/p>\n<p style=\"text-align: center;\">R=[1\/(s\/d)]+{1-[1\/(s\/d)]}\u00b7R<sub>p<\/sub><\/p>\n<p>Factorul R depinde deci de raportul dintre interaxul prezent \u00eentre piloti, diametrul pilotilor si factorul R<sub>p<\/sub> ce tine cont de efectul arc.<\/p>\n<p><strong>ANALIZA ACTIUNII SEISMICE<br \/>\n<\/strong>La verific\u00e3rile la St\u00e3ri Limit\u00e3 Ultime stabilitatea taluzurilor, tin\u00e2nd cont de actiunea seismic\u00e3, este realizat\u00e3 cu metoda pseudo-static\u00e3. Pentru terenurile sub actiunea sarcinii ciclice ce pot dezvolta presiuni interstiziale ridicate este considerat\u00e3 o crestere \u00een procente a presiunilor neutrale care tine cont de acest factor de pierdere de rezistent\u00e3.<br \/>\nLa finalul analizei actiunii seismice, la verific\u00e3rile la st\u00e3ri limit\u00e3 ultime, sunt considerate urmatoarele forte statice echivalente:<\/p>\n<p>F<sub>H<\/sub>=K<sub>x<\/sub>\u00b7W<br \/>\nF<sub>V<\/sub>=K<sub>y<\/sub>\u00b7W<\/p>\n<p>\u00cen care:<\/p>\n<ul>\n<li><strong>F<sub>H<\/sub><\/strong>\u00a0si \u00a0<strong>F<sub>V <\/sub><\/strong>respectiv componenta orizontal\u00e3 si componenta vertical\u00e3 a fortei de inertie aplicat\u00e3 \u00een baricentrul f\u00e2siei<\/li>\n<li><strong>W<\/strong> greutatea f\u00e2siei<\/li>\n<li><strong>K<sub>x<\/sub><\/strong> Coeficient seismic orizontal<\/li>\n<li><strong>K<sub>y<\/sub><\/strong> Coeficient seismic vertical<\/li>\n<\/ul>\n<p style=\"text-align: justify;\"><strong>Search of the critical sliding surface<br \/>\n<\/strong>In the presence of homogeneous mediums there are no available methods for detecting the critical sliding surface and must examine a large number of potential surfaces.<br \/>\nIn case of circular shape surfaces, the search becomes more simple, since after placing a mesh of centers consisting of m rows and n columns will be examined all surfaces having as center the generic node of the mesh m\u00b4n and variable radius in a given range of values that examine surfaces kinematically admissible. .<\/p>\n<p style=\"text-align: justify;\"><strong>Stabilizarea taluzurilor prin utilizarea pilotilor<br \/>\n<\/strong>Realizarea unei cortine de piloti, pe taluz, este necesar\u00e3 pentru a creste rezistenta la forfecare pentru anumite suprafete de alunecare. Interventia poate urma unei stabiliz\u00e3ri deja stabilite, pentru care se cunoaste suprafata de alunecare sau este proiectat\u00e3 in raport cu presupuse suprafete de cedare, cele mai probabile. Oricare ar fi cazul, se lucreaz\u00e3 consider\u00e2nd o mas\u00e3 de teren \u00een miscare pe o baz\u00e3 stabil\u00e3 pe care se vor amplasa si pilotii.<\/p>\n<p style=\"text-align: justify;\">Terenul, \u00een cele dou\u00e3 zone, are o influent\u00e3 diferit\u00e3 pe elementul monoaxial (pilot): de tip solicit\u00e3ri pe \u00een partea superioar\u00e3 (pilot pasiv \u2013 teren activ) si de tip rezistiv \u00een partea de jos a acestuia (pilot activ \u2013 teren pasiv). Din aceast\u00e3 interferent\u00e3, \u00eentre \u201cbarier\u00e3\u201d si masa \u00een miscare, se nasc actiunile stabilizante ce trebuie s\u00e3 urm\u00e3reasc\u00e3:<\/p>\n<ol>\n<li style=\"text-align: justify;\">s\u00e3 confere taluzului un cieficient de sigurant\u00e3 mai mare dec\u00e2t cel initial;<\/li>\n<li style=\"text-align: justify;\">S\u00e3 fie absorbited de lucrare garant\u00e2nd integritatea acesteia (tensiunile interne, ce deriv\u00e3 din solicit\u00e3rile maxime transmise diverselor sectiuni ale pilotului singular, trebuie s\u00e3 fie mai mici dec\u00e2t cele admisibile ale materialului) si s\u00e3 fie mai mici dec\u00e2t sarcina limit\u00e3 ce poate fi suportat\u00e3 de teren, calculat\u00e3 cansider\u00e2nd interactiunea (pilot-teren).<\/li>\n<\/ol>\n<p style=\"text-align: justify;\"><strong>Sarcina limit\u00e3 aferent\u00e3 interactiunii dintre piloti si terenul lateral<br \/>\n<\/strong>\u00cen diversele categorii de teren care nu au un comportament omogen, deform\u00e3rile corespunz\u00e3toare zonei de contact nu sunt legate \u00eentre ele. Deci, neput\u00e2nd asocia materialului un model de comportament perfect elastic, \u00een general se impune ca miscarea de mas\u00e3 s\u00e3 fie \u00een stratul initial si ca terenul adiacent pilotilor s\u00e3 fie \u00een faza maxim\u00e3 de plasticizare acceptat\u00e3, dincolo de care se poate verifica efectul nedorit de curgere a materialului, travers\u00e2nd cortina de piloti, \u00een spatiul.<\/p>\n<p>&nbsp;<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-134009 \" src=\"https:\/\/www.geostru.eu\/wp-content\/uploads\/2016\/06\/pali-1.jpg\" alt=\"pali\" width=\"670\" height=\"372\" srcset=\"https:\/\/www.geostru.eu\/wp-content\/uploads\/2016\/06\/pali-1.jpg 747w, https:\/\/www.geostru.eu\/wp-content\/uploads\/2016\/06\/pali-1-300x167.jpg 300w, https:\/\/www.geostru.eu\/wp-content\/uploads\/2016\/06\/pali-1-500x278.jpg 500w\" sizes=\"(max-width: 670px) 100vw, 670px\" \/><\/p>\n<p style=\"text-align: justify;\">Impun\u00e2nd ca sarcina limit\u00e3 absorbit\u00e3 de teren s\u00e3 fie egal\u00e3 cu cea asociat\u00e3 conditiei limit\u00e3 ipotizat\u00e3 si ca \u00eentre doi piloti consecutivi, ca urmare a \u00eempingerii active, se instaureaz\u00e3 un tip de efect arc, autorii T. Ito si T. Matsui (1975) au dedus o relatie ce permite determinarea sarcinii limit\u00e3. S-a ajuns la aceasta f\u00e3c\u00e2nd referire la schema static\u00e3, desenat\u00e3 \u00een figura precedent\u00e3 si la ipotezele mentionate anterior care se reafirm\u00e3 schematic.<\/p>\n<ul style=\"text-align: justify;\">\n<li>Sub actiunea \u00eempingerilor active ale terenului se formeaz\u00e3 dou\u00e3 suprafete de alunecare localizate \u00een corespondenta liniilor AEB si A\u2019E\u2019B<\/li>\n<li>irectiile EB si E\u2019B\u2019 formeaz\u00e3 cu axa x unghiurile +(45 + \u03c6\/2) respectiv \u2013(45 + \u03c6\/2).<\/li>\n<li>Volumul de teren, cuprins \u00een zona delimitat\u00e3 de v\u00e2rfurile AEBB\u2019E\u2019A\u2019 are un comportament plastic, si este deci permis\u00e3 aplicarea criteriului de cedare Mhor-Coulomb;<\/li>\n<li>Presiunea activ\u00e3 a terenului actioneaz\u00e3 peplanul A-A\u2019;<\/li>\n<li>Pilotii au o ridicat\u00e3 rigiditate, \u00eendoire si forfecare.<\/li>\n<\/ul>\n<p style=\"text-align: justify;\">Expresia de mai jos face referire la ad\u00e2ncimea generic\u00e3 Z, aferent\u00e3 unei grosimi unitare a terenului:<\/p>\n<p style=\"text-align: center;\">P(Z)=C\u00b7D<sub>1<\/sub>\u00b7(D<sub>1<\/sub>\/D<sub>2<\/sub>)^(k<sub>1<\/sub>)\u00b7{1\/[(N<sub>\u03c6<\/sub>\u00b7tan\u03c6)\u00b7(e^(k<sub>2<\/sub>)-2(N<sub>\u03c6<\/sub>)^(0.5)\u00b7tan\u03c6-1)]}-C\u00b7[D<sub>1<\/sub>\u00b7k<sub>3<\/sub>-D<sub>2<\/sub>\/(N<sub>\u03c6<\/sub>)^(0.5)+\u03b3\u00b7Z\/{N<sub>\u03c6<\/sub>-[D<sub>1<\/sub>\u00b7(D<sub>1<\/sub>\/D<sub>2<\/sub>)^(k<sub>1<\/sub>)\u00b7e^(k<sub>2<\/sub>)-D<sub>2<\/sub>]}<\/p>\n<p>unde simbolurile utilizate au urm\u00e3toarea semnificatie:<\/p>\n<p><strong>C <\/strong>= coeziune teren;<br \/>\n<strong>\u03c6<\/strong> = unghi de frecare teren;<br \/>\n<strong>\u03b3<\/strong> = greutate specific\u00e3 teren;<br \/>\n<strong>D<\/strong><strong><sub>1<\/sub><\/strong> =\u00a0distanta\/interax dintre piloti;<br \/>\n<strong>D<\/strong><strong><sub>2<\/sub><\/strong> = spatiu liber \u00eentre doi piloti consecutivi;<br \/>\n<strong>N<\/strong><strong><sub>\u03c6<\/sub><\/strong> = tag<sup>2<\/sup>(\u03c0\/4 + \u03c6\/2)<\/p>\n<p>K<sub>1<\/sub>=N<sub>\u03c6<\/sub>^(0.5)\u00b7tan\u03c6+N<sub>\u03c6<\/sub>-1<br \/>\nK<sub>2<\/sub>=[(D<sub>2<\/sub>-D<sub>1<\/sub>)\/D<sub>2<\/sub>]\u00b7N<sub>\u03c6<\/sub>\u00b7tan(\u03c0\/8 + \u03c6\/4)<br \/>\nK<sub>3<\/sub>=[2\u00b7tan\u03c6+2\u00b7N<sub>\u03c6<\/sub>^(0.5)+1\/N<sub>\u03c6<\/sub>^(0.5)]\/[N<sub>\u03c6<\/sub>^(0.5)\u00b7tan\u03c6+N<sub>\u03c6<\/sub>-1]<\/p>\n<p>Forta total\u00e3, aferent\u00e3uni strat de teren \u00een miscare de grosime H, a fost obtinut\u00e3 integr\u00e2nd expresia anterioar\u00e3.<\/p>\n<p>\u00cen prezenta terenurilor granulare (conditie drenat\u00e3), \u00een care se poate lua C=0, expresia devine<\/p>\n<p style=\"text-align: center;\">P(Z)=[0.5\u00b7\u03b3\u00b7H^(2)]\/{N<sub>\u03c6<\/sub>[D<sub>1<\/sub>\u00b7(D<sub>1<\/sub>\/D<sub>2<\/sub>)^(k<sub>1<\/sub>)\u00b7e^(k<sub>2<\/sub>)-D<sub>2<\/sub>]}<\/p>\n<p>Pentru terenuri coezive (conditii nedrenate), cu \u03c6 = 0 si C \u2260 0 avem:<br \/>\nP(Z)=C\u00b7{D<sub>1<\/sub>\u00b7[3\u00b7ln(D<sub>1<\/sub>\/D<sub>2<\/sub>)+(D<sub>1<\/sub>-D<sub>2<\/sub>)\/(D<sub>2<\/sub>)\u00b7tan\u03c0\/8]-2\u00b7(D<sub>1<\/sub>-D<sub>2<\/sub>)}+\u03b3\u00b7z\u00b7(D<sub>1<\/sub>-D<sub>2<\/sub>)<br \/>\nP=\u017f<sub>0,H<\/sub>P(z)\u00b7dz<br \/>\nP(Z)=C\u00b7H\u00b7{D<sub>1<\/sub>\u00b7[3\u00b7ln(D<sub>1<\/sub>\/D<sub>2<\/sub>)+(D<sub>1<\/sub>-D<sub>2<\/sub>)\/(D<sub>2<\/sub>)\u00b7tan\u03c0\/8]-2\u00b7(D<sub>1<\/sub>-D<sub>2<\/sub>)}0.5\u00b7\u03b3\u00b7H^(2)\u00b7(D<sub>1<\/sub>-D<sub>2<\/sub>)<\/p>\n<p style=\"text-align: justify;\">Dimensionarea cortinei de piloti, ce trebuie s\u00e3 ofere taluzului o crestere a coeficientului de sigurant\u00e3 si s\u00e3 garanteze integritatea mecanismului pilot-teren, este destul de problematic\u00e3. Tin\u00e2nd cont de complexitatea expresiei sarcinii P, influentat\u00e3 de diversi factori legati at\u00e2t de caracteristicile mecanice ale terenului c\u00e2t si de geometria lucr\u00e3rii, nu este usor s\u00e3 se ajung\u00e3 la solutia optim\u00e3 cu o singur\u00e3 prelucrare. Pentru a atinge acest scop sunt necesare mai multe tentative menite<\/p>\n<ul>\n<li style=\"text-align: justify;\">S\u00e3 g\u00e3seasc\u00e3, pe profilul topografic al taluzului, pozitia care s\u00e3 garanteze, al\u00e3turi de alte conditii, o distributie a coeficientilor de sigurant\u00e3 mai reconfortant\u00e3<\/li>\n<li style=\"text-align: justify;\">S\u00e3 determine distributia planimetric\u00e3 a pilotilor, caracterizat\u00e3 de raportul dintre interax si distanta dintre piloti (D2\/D1), ce permite exploatarea optim\u00e3 a rezistentei complexului pilot-teren; S-a stabilit exeperimental c\u00e3, excluz\u00e2nd cazurile limit\u00e3 (D2 = 0 P\u2192 \u221e si D2 = D1 P\u2192 valoare minim\u00e3), valorile cele mai potrivite sunt cele pentru care raportul este cuprins \u00eentre 0,60 si 0,80<\/li>\n<li style=\"text-align: justify;\">S\u00e3 considere posibilitatea de a insera mai multe siruri de piloti si eventual, \u00een caz afirmativ, s\u00e3 se calculeze, pentru r\u00e2nduri succesive, pozitia care d\u00e3 mai multe garantii privind siguranta si economia de materiale<\/li>\n<li style=\"text-align: justify;\">S\u00e3 adopte tipul de blocaj cel mai potrivit ce permite obtinerea unei distributii mai regulate a solicit\u00e3rilor; s-a constatat experimental c\u00e3 blocajul care \u00eempiedic\u00e3 rotirea la cap\u00e3tul pilotului este cel mai potrivit \u00een acest scop.<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>Extract of the technical report of\u00a0<a style=\"color: #ffff00;\" href=\"https:\/\/www.geostru.eu\/ro\/shop\/software-ro\/software-geologia-ro-2\/stabilitatea-taluzurilor-slope\/\">SLOPE<\/a>[\/vc_column_text][\/vc_column][\/vc_row][vc_row bg_type=&#8221;bg_color&#8221; bg_color_value=&#8221;#f4f4f4&#8243;][vc_column width=&#8221;1\/2&#8243;][vc_single_image image=&#8221;138181&#8243; img_size=&#8221;medium&#8221;][\/vc_column][vc_column width=&#8221;1\/2&#8243;][vc_column_text]Software pentru stabilitatea taluzurilor \u00een \u00een soluri af\u00e2nate sau st\u00e2ncoase cu metodele tradi\u021bionale ale geotehnicii (Echilibrul Limita), \u0219i metoda Elementelor Discrete cu care se poate calcula deplasarea taluzului \u0219i se poate examina ruptura progresiva.<br \/>\n\u00een condi\u021bii seismice realizeaz\u0103 at\u00e2t analiza statica cat \u0219i analiza dinamica.<\/p>\n<p><a href=\"https:\/\/www.geostru.eu\/shop\/software-ro\/software-geologia-ro-2\/stabilitatea-taluzurilor-slope\/?lang=ro\" target=\"_blank\" rel=\"noopener\">SLOPE<\/a>[\/vc_column_text][\/vc_column][\/vc_row]<\/p>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>[vc_row][vc_column][vc_column_text] Stabilitatea taluzurilor Taluzul este o suprafat\u00e3 \u00eenclinat\u00e3 cu panta, \u00een general, mai mare de 45\u00b0, realizat\u00e3 \u00een special antropic, care m\u00e3rgineste un rambleu sau un debleu. Alunec\u00e3rile de teren sunt o categorie de fenomene naturale de risc, ce definesc procesul de deplasare, miscarea propriu\u2011zis\u00e3 a rocilor sau depozitelor de pe versanti, c\u00e2t si forma&hellip;<\/p>\n","protected":false},"author":216,"featured_media":22676,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[592,591,589,861,80],"tags":[598],"class_list":["post-22695","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-articole-geotehnic","category-articole-pentru-geologie","category-inginerie-civila","category-pubblicazioni-ro","category-publicatii","tag-stabilitatea-taluzurilor","category-592","category-591","category-589","category-861","category-80","description-off"],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v25.0 (Yoast SEO v25.0) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Stabilitatea 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