Finite Element Analysis of the Stability of Tunnel Surrounding Rock with Weak Rock Layer

Transcription

1 Vol., No. 2 Modern Appled Sene Fnte Element Analyss of the Stablty of Tunnel Surroundng Rok wth Weak Rok Layer Yangsong Zhang Nanjng Unversty of Sene and Tehnology, Nanjng 294, Chna Tel: E-mal: zysnj8@26.om Xaozhao L Nanjng Unversty, Nanjng 29, Chna Tel: E-mal: lxz@nju.edu.n The researh s fnaned by the Natural Sene Foundaton of Chna (No ). (Sponsorng nformaton) Abstrat The evaluaton of loal stablty of the tunnel surroundng rok mass wth weak rok layer s very mportant for the eonomy and seurty of the tunnel onstruton. Based on the rok tunnel geologal ondtons n the onstruton, the fnte element model of the tunnel surroundng rok mass stablty analyss wth weak rok layer s establshed n the artle by seletng the ABAQUS program lnear D-P materals model as the gness yeld rteron. The omputaton result ndates that the explt dynam analyss program ould smulate the whole proess of the nstablzaton and falure of the weak rok layer, and avod the onvergene exstng n the general fnte element omputaton, and the analyss model and program ould offer effetve measure for the analyss of loal stablty of the tunnel surroundng rok mass wth weak rok layer. Keywords: Rok tunnel, Weak rok layer, Explt fnte element analyss, Stablty. Introduton The empral method and the numeral analyss method are two man methods to analyze the stablty of the tunnel surroundng rok mass at present. The empral method s to manly qualtatvely analyze the stablty of tunnel surroundng rok mass aordng to the qualty lassfaton result of roks, and the qualty lassfaton methods extensvely used n the world nlude the Geomehans Classfaton System (RMR, Benawsk, 989), the Q-system (Barton et al., 974 & Barton, 22), the Geologal Strength Index (GSI, Hoek and Brown, 997), and the Chnese natonal standard BQ lassfaton method whh s extensvely used n Chna (The Mnstry of Water Resoures People Republ of Chna, 995). These lassfaton methods are the results of researhes n many tunnel ases, and have been appled n many evaluatons about the stablty of pratal tunnel surroundng rok mass. But these methods ould not quanttatvely ompute the stress redstrbuton aroused n tunnellng works (Basarr et al., 25), and ould not reasonably onsder the loal stablty of unequal tunnel surroundng roks wth weak rok layer. On the other hand, the fnte element method ould offer the dsplaement of the surroundng rok mass after tunnel s exavated, the stress redstrbuton, the plast zone dstrbuton, and other useful nformaton, whh an help to quanttatvely evaluate the stablty of the surroundng rok mass (Zhu Weshen et al., 2 & Basarr et al., 25). However, smlarly, the reasonablty of the results omputed by many numeral methods suh as fnte element method depends on whether the spae dstrbuton of rok medum n the establshed numeral analyss models s lose to the atual stuaton to large extent, and the reasonablty of nput parameters n varous rok mass omputatons. For the surroundng rok mass that the rok mass have good qualty and hgh strength, when analyzng the stablty of tunnel surroundng rok mass by the fnte element method, the seurty oeffent s often used to denote the fator of safety of stablty, but to solve the fator of safety of the stablty of tunnel surroundng rok mass, the strength reduton method s manly adopted at present (Zheng Yngren and Zhao Shangy, 25). But when omputng the loal stablty of surroundng rok mass wth weak rok layer, and the strength parameter of rok mass s not redued, the weak rok layer may be falured loally, and t s very mportant to manly study when the weak rok layer begns to beome nto nstablzaton and falure, and the nfluenes of the whole stablty of tunnel surroundng rok mass after 22

2 Modern Appled Sene Deember, 29 the weak rok layer s falured, and the loal supportng opportunty, and the supportng effet. There are not systemat researh results about these problems at present. In the artle, takng geologal ondtons of Yuntashan Road Tunnel n Lanyungang of Jangsu, Chna, as the example, the fnte element omputaton analyss method about the loal stablty of the tunnel surroundng rok wth weak rok layer s dsussed as follows. 2. Explt fnte element analyss of the whole proess of nstablzaton and falure of tunnel surroundng rok mass 2. Instablzaton rtera of tunnel surroundng rok mass At present, the rteron that the fnte element method s adopted to ompute extreme status of nstablzaton and ollapsed of rok-sol mass nludes followng knds. () The dstrbuton of plast zone. The sze of the plast zone of surroundng rok mass n exavang s one standard to evaluate the stablty of surroundng rok mass (Ferrero Anna Mara, Mglazza Mara, Gan Gan Paolo, 24). But for tunnels, the onept of the sze of the plast zone of surroundng rok mass or whether t s onneted or not s not spef lke the slope and the spef borderlnes are dffult to be onfrmed. (2) The omputatng that the fnte element s not onvergent ndates that the rok-sol mass has been destroyed (Dawson E.M., Roth W. H., 999 & Grffths D.V., Lane, P.A., 999). Aordng to ths standard, dfferent fnte element programs and dfferent onvergene standards wll produe dfferent omputaton results. And n the fnte element smulaton analyss of tunnellng, the result of the general fnte element program s not onvergent often, so the further hange of the surroundng rok mass status after loal destroyng an not be known. () The sgn that the rok-sol mass s ollapsed should be that the slde moves nfntely, and the slde surfae of rok-sol mass and the dsplaement hange and development nfntely. If the numeral method an ompute the deformaton of surroundng rok mass, and follow the whole proess of the deformaton and nstablty of surroundng rok mass, so ths rule s very good. And t an montor varous ponts of the surroundng rok mass of dfferent lasses n dfferent parts of the tunnel, whh an not only know the loal nstablty, but know the total nstablty ndued by the loal nstablty. It speally suts for the analyss and judgment of the loal stablty of tunnel surroundng rok mass wth weak rok layer. 2.2 Consttutve model of rok mass Mohr-Coulomb strength rule and the Druker-Prager strength rule are two knds of usual rules n the rok-sol mass omputaton. The strength parameter of the Mohr-Coulomb s easly obtaned usually, but n the extreme analyss of rok-sol mass, ts omputaton result often s not onvergent at the sharp orner. In the artle, the lnear Druker-Prager model s adopted. The lnear Druker-Prager yeldng funton and the plast potental energy respetvely are (ABAQUS In, 26) F t p tan d () G t p tan (2) Here, 9 t q, r ( S S S, S pi 2 K K q 2 (, f) s the slope of the lnear yeldng plate on the p t stress plane, and t s usually alled as the frton angle of materals. d s the ohesve strength of materals, and d tan, s the unaxal ompressve yeldng stress, and K(, f ) s the rato between the unaxal extenson yeldng stress and the unaxal ompressve yeldng stress, so t ontrol the dependene of the mddle man stress of the yeldng plane., f ) s the dlaton angle n the p t plane. ( The Mohr-Coulomb rule an be denoted as (ABAQUS In, 26) ( ) sn 2 os () For the traxal ompresson, the formula () an be rewrote as tan tan ( ) (4) 2 tan tan 6 2

3 Vol., No. 2 Modern Appled Sene By Comparng the formula () wth the formula (4), and one and the Mohr-Coulomb rules are tan 24 6sn sn orrespondng wth the Druker-Prager ompresson (5) os 2 (6) sn In the same way, and orrespondng wth the Druker-Prager tensle one and the Mohr-Coulomb rules respetvely are 6sn tan (7) ( sn) os(6 tan ) (8) tan K (9) tan Ft the average value of the ompresson one and the tensle one of the Druker-Prager yeldng rule wth the Mohr-Coulomb rule, and take the average tan value of the formula (5) and the formula (7) to ompute K(, f ) aordng to the formula (9), and.778 K(, f ), and n the same way, K(, f ) ontrols the dependene of the mddle man stress of the yeldng plane. Large numerous of omparsons and omputatons ndated that the parameters omputed by the lnear Druker-Prager yeldng rule and above methods and Mohr-Coulomb had good fttng preson. 2. Analyss approahes In general fnte element analyss, there are three methods to smulate the tunnellng,.e. () gradually redung the elastty modulus of the exavatng rok mass, (2) adoptng the kllng element or removng element method, () substtutng the rok mass n exavatng tunnels by the fxed boundary ondtons, and frst omputng the ntal stress to balane the reverse stress of above borderlnes, and n subsequent omputaton, puttng the borderlne reverse funton on the respondng nodes, and removng orrespondng fxed borderlne ondtons on the tunnellng plane, and omputng the ground stress balane, and n subsequent omputaton, gradually redue the reverse stress on the tunnellng fae to smulate the stress release n tunnellng aordng to ertan proporton. In ABAQUS/Explt analyss, above two methods an not obtan satsfatory exavatng modelng effet. Though the thrd method s omplex, but t fts for the ABAQUS/Explt analyss, and t s onvenent to aurately ontrol the stress release. Aordng to the surroundng rok mass ondton, eah step to exavate tunnel s.m, and the detaled smulaton proess nludes followng steps. () Compute the reverse fores of varous nodes on the walls of the exavatng tunnel. It only needs to mplement the fxed borderlne ondtons on the tunnellng fae n the step of the ntal geostat stress balane, so the reverse fores of varous nodes an be obtaned. (2) Implement the reverse fores of varous nodes n the omputaton of frst step on the orrespondng nodes to ompute the ntal geostat stress balane agan. () Gradually redue the reverse fores of varous nodes on the tunnel surfaes to zero step by step, to smulate the stress release of rok mass n eah tme. The fnal smulaton omputaton nludes the release of the reverse fores of the nodes on the surfae of surroundng rok mass n front of the tunnel. The frst step s mplemented n ABAQUS/Standard, and the seond step and the thrd step are mplemented ontnually n ABAQUS/Explt.. Example analyss. Geologal ondtons and physal mehanal parameters of surroundng rok masses The omputaton anttype s the surroundng rok mass seton of the tunnel, manly nludes the sold metamorph roks, and the saturated unaxal ompressve strength of roks s R C =5~MPa. For two man jonts strkes are NE and NW n the rok mass, the jont plane s planar and oarse, and presents lose-partng openng status wthout fllng. The shstose strutural plane ourrene average dp s 55, and the average oblquty angle s 28. Some parts wth

4 Modern Appled Sene Deember, 29 the green shst weak rok layer unvel, and the saturated unaxal omprehensve strength of roks s R C =5~7MPa, and the shstose strutural plane of rok mass grows. The weak rok dstrbute as the nteralated status along the shstose strutural plane dreton. The feld survey shows that when the weak rok layer s dstrbuted on the top of the tunnel, f the loal support measure s not adopted, the loal nstablzaton and falure of surroundng rok mass easly our. Aordng to the feld survey, the geometr relatonshp model between the weak rok dstrbuton and the tunnel s seen n Fgure. The physal mehanal parameters onfrmed by the modfed bas qualty ndex [BQ] of surroundng rok masses are seen n Table, and the Table also shows the nternal frton angle and the ompressve ntal yeldng stress of the lnear Druker-Prager rule. For the lnear Druker-Prager rule n the ABAQUS program, to ensure that the yeldng plane s out-extrusve, the value of K should equal or exeed.778, so when value of k onfrmed by the formula (6) s less than.778, K=.778. Take nonassoated flow rules, suppose the expanson angle s (, f ) =/4 (Hok and Brown, 997)..2 Fnte element analyss model In the omputaton, for the model, the length s 2m (x axs), the heght s 2m (z axs), the depth s 45m (y axs), the span of the tunnel s 6m, and the heght of the tunnel s 9.5m, and the smulated exavatng depth of the tunnel s 5m, and whole setons are dug. The length from the top of the tunnel to the top of the model s 4m, and the rok mass of 2m overng on t adopts the average press on the surfae of the model to be smulated. As seen n Fgure 2, the model s dvded nto node lnear tetrahedron elements and 285 nodes.. Results of omputaton and analyss Aordng to the numeral smulaton results, through observng the vertal dsplaement of the tunnel top and the dstrbuton of the plast zone of surroundng rok masses, followng rules an be summarzed... Vertal dsplaement of tunnel top The dstrbuton of the fnal vertal dsplaement (U) of tunnel surroundng rok mass obtaned n the fnte element omputaton s seen n Fgure. From Fgure, the vertal dsplaement value from the top of the tunnel n the weak rok mass ([BQ]=24) dstrbuton zone obvously exeeds the orrespondng values surroundng the sold rok zone ([BQ]=5). The maxmum of the vertal dsplaement of the tunnel top s at the node A, and t s 7.2mm n the weak rok layer, and the mnus denotes the dsplaement dreton downwards, whh s observe of the dreton of Z axs. But the dsplaements n the sold rok zone of the tunnel top are small, for example, the vertal dsplaement of the node C far from the weak rok dstrbuton s 6.8mm. In the fnte smulaton omputaton of tunnellng, the load release proporton fator (LPD) and the omputaton tme have same meanngs. Wth the nrease of the exavatng step omputaton tme, the node fore on the exavatng borderlne gradually redues to zero. So from the result of the fnte element omputaton, the relatonshp between the node dsplaement on the exavatng plane and the load release proporton fator an be easly obtaned. Fgure 4 shows the relatonshp urve between the vertal dsplaement and the load release proporton fator of three plaes on the top of tunnel. Obvous nflexon ours n the urve of the node A (weak rok layer) wth the nrease of the load release proporton fator when LPD s lose to.9,.e. the dsplaement nreases qukly, so aordng to the result of the fnte element omputaton, omparng wth the extreme status rule 2, f any support measure s adopted, the weak rok layer on the top of tunnel wll be ollapsed. That aords wth atual stuaton, n the tunnellng onstruton of Yuntashan n Lanyungang, n the sold II-lass surroundng rok mass, beause the qualty of rok mass was good, the systemat prmary support had not been adopted aordng to relatve standards, and the stablty was good when the weak rok layer ddn t exst, and the deformaton of surroundng rok mass was small, but for the same sold II-lass surroundng rok mass, when the top of tunnel had the weak rok layer wth bg depth (~m) and effetve loal support had not been adopted, several ollapses ourred n the weak rok surroundng layer on the top of tunnel n ertan tme after the tunnel was exavated. From Fgure 4, the vertal dsplaements of the node B and the node C n the sold rok zone are obvously less than the vertal dsplaement of the node A, and beause the node B s lose to the edge of the weak rok layer, the vertal dsplaement s larger than the node C far from the weak rok mass beause of the nfluene of the weak rok plast falure. The vertal dsplaements of the node C and the node B nrease slowly, whh ndates that they have not aheved the extreme status...2 Plast zone of surroundng rok mass Fgure 5 shows the dstrbuton of the plast zone of surroundng rok mass. From Fgure 5, the plast zone ours n the top of tunnel and the upper weak rok layer on the exavatng plane. The sold rok dstrbuton zones all have not aheved the plast falure. From the development proess of the plast zone, when the load proporton fator s.9, obvous plast varane begns n the weak rok layer, whh aords wth the tme when the nflexon of the vertal 25

5 Vol., No. 2 Modern Appled Sene dsplaement-load proporton fator urve of the node A, and that ndates that the quk nrease of dsplaement s the ndued by the obvous plast varane n surroundng rok mass. 4. Conlusons Combnng wth the lnear Druker-Prager yeldng rule, the ABAQUA/Explt program s adopted to analyze the stablty of the tunnel surroundng rok mass wth the weak rok layer. By the researh, followng onlusons an be obtaned. () The numeral analyss program n the artle an be used to ompute the whole proess of the deformaton and falure of the tunnel surroundng rok mass, and t an avod the problem that the results of the fnte element omputaton s not onvergent, so t speally suts for the omputaton of the stablty of the tunnel surroundng rok mass wth weak rok layer. (2) It s reasonable and feasble to apply the ABAQUS/Explt program to ompute and adopt the rule that the deformaton nreases qukly as the extreme status of the nstablzaton and falure of tunnel surroundng rok mass. On the one hand, the omputaton program an ensure to obtan the nflexon that the dsplaement qukly nreases, and on the other hand, the results of the omputaton and judgment are oherent wth the atual stuaton. () In the artle, the qualty lassfaton standard of rok mass s adopted to evaluate the strength parameters of Mohr-Coulomb rule, and these parameters are onverted nto the strength parameters of the lnear Druker-Prager yeldng rule by the method n the artle. Then they are used to ompute the stablty and the dsplaement of tunnel surroundng rok mass, and the omputaton results s oherent wth the atual survey result. Referenes ABAQUS In. (26). ABAQUS User s Manual, Verson 6.6. Barton, N., Len, R., Lunde, J. (974). Engneerng lassfaton of rok masses for the desgn of tunnel support. Rok Meh. No.6(4). P Basarr, H., Ozsan, A., Karakus, M. (25). Analyss of support requrements for a shallow dverson tunnel at Guledar dam ste, Turkey. Engneerng Geology. No.8. P.-45. Benawsk, Z.T. (989). Engneerng Rok Mass Classfaton: A Complete Manual for Engneers and Geologsts n Mnng, Cvl, and Petroleum Engneerng. Wley, New York. 25 pp. Dawson E.M. and Roth W. H. (999). Dresher A. Slope stablty analyss by strength reduton. Geotehnque. No.49 (6). P Ferrero Anna Mara, Mglazza Mara, Gan Gan Paolo. (24). Analyss of tunnel stablty: omparson between ontnuous and dsontnuous approahes. Int J Rok Meh. Mn. S. No.4(). CD-ROM. P.-6. Hoek E and Brown ET. (997). Pratal estmates of rok mass strength. Int J Rok Meh Mn S Geomeh Absrr. No.4(8). P The Mnstry of Water Resoures People Republ of Chna. (995). The Chnese Standards-Standard for engneerng lassfaton of rok masses (GB528-94). Bejng: Chna Plannng Press (n Chnese). Zheng, Yngren and Zhao, Shangy. (25). Lmt state fnte element method for geotehnal engneerng analyss and ts applatons. Chna vl engneerng journal. No.8(). P.9-4 (n Chnese). Zhu, Weshen, L, Shua, L, Shuhen, et al. (2). Systemat numeral smulaton of rok tunnel stablty onsderng dfferent rok ondtons and onstruton effets. Tunnellng and Underground Spae Tehnology. No.8. P Table. Physal mehan parameters based on the modfaton of the bas qualty ndex [BQ] of surroundng rok mass Type of rok [BQ] Class of rok mass Deformaton modulus E mass (GPa) Passon rato Densty of gravty (kn/m ) Mohr-Coulomb rteron ( - ) (MPa) ( - ) Druker-Prager rteron (MPa) Sold rok 5 II Weak rok 24 V

6 Modern Appled Sene Deember, 29 Fgure. Weak Rok layer on the Top of the Tunnel (the lnes n the model present the range of weak rok layer) Fgure 2. Fnte Mesh of the Tunnel Computaton Model Fgure. Vertal Dsplaement U of Tunnel Surroundng Rok mass (Unt: m) (Nodel A: weak rok layer, Nodel B: sold roks near to weak rok layer, Nodel C: sold roks far from weak rok layer) Fgure 4. Relatonshp Curve between Vertal Dsplaement of Surroundng Rok Mass on the Top of Tunnel and the Load Proporton fator (LPD) 27