THE IMPACT OF EARTHQUAKES OF TUNNEL LININGS: A CASE STUDY FROM THE HANOI METRO SYSTEM

Transcription

1 Iteratioal Joural of GEOMATE, Ja., 18 Vol.14, Issue 41, pp Geotec., Cost. Mat. & Ev., DOI: IN: (Prit), (Olie), Japa THE IMPACT OF EARTHQUAKE OF TUNNEL LINING: A CAE TUDY FROM THE HANOI METRO YTEM Gospodarikov Alexadr 1 1, * ad Thah Nguye Chi 1 ait Petersburg Miig Uiversity, ait Petersburg, Russia Federatio; Haoi Uiversity Miig ad Geology, Haoi, Vietam *Correspodig Author, Received: 1 Nov. 17, Revised: 8 Dec. 17, Accepted: Dec. 17 ABTRACT: At preset, systems of ifrastructure are built ad developed very strogly i Haoi. The metro tuels system is also beig desiged ad built i Haoi to meet the requiremets of ecoomic ad social developmet. The paper uses the Wag's method, Pezie & Wu's method, HRM method ad a two dimesioal umerical aalysis method by Abaqus software to evaluate the impact of the strogest earthquake that could occur i Haoi to the tuel liig of Haoi metro system, this impact could be the iteral forces ad state stress o the tuel liig. Based o results obtaied from assessig the impact of earthquakes to the tuel liig i the Haoi metro system, this paper has compared ad commeted to these results for the purpose of fidig the most accurate results about the impact of earthquakes o the tuel liig i the Haoi metro system. These results ad commets will be used i the desig ad costructio tuel i the Haoi metro system uder the impact of the strogest earthquake that could occur i Haoi. Keywords: Tuel liig, earthquake, state stress, iteral forces. 1. INTRODUCTION Earthquakes are atural pheomeo that is difficult to predict ad accurately calculates its impact o works withi its limit of ifluece. The impact of earthquakes o the works ca be do the deformatio of works or works may be displaced. Works may be chage or completely destroyed. Haoi is the capital of Vietam, where has got very may people ad there are importat works here. At preset, the metro system that has bee desiged ad built i Haoi. Haoi is located ear og La - Die Bie ad Red River faults with the strogest earthquake M W = 6.5 richter [1]. Based o the geological ad hydro-geological coditios i the cetral part of Haoi ad the parameters of earthquake, that may occur i the Haoi area, this paper has bee study ad evaluate of the impact of the strogest earthquake o the liig tuel i Haoi metro system.. PARAMETER OF EARTHQUAKE, OIL AND TUNNEL UBWAY IN HANOI The groudwater level i Haoi is quite high, i the cetral area of Haoi, the hydrogeological ad geological coditios are as follows: the groud water level is three meters below the surface; distributed from the groud surface to the bedrock at a depth of 48 m ad there are usually six layers of soils. All parameters of layers soil i Haoi ceter i Table 1 ad i Fig.1. m 6.3 m Tuel Bed rock Fig.1 Layers soils of cosidered sectio oil Layer 1 - Backfill m oil Layer - oft clay-1.1 m oil Layer 3 - tiff lea clay m oil Layer 4 - Dese clay sad -1.5 m oil Layer 5 - Very dese clay sad -11. m oil Layer 6 - Coarse sad with Gravel -7. m Parameters of tuel i the Haoi metro system []: The tuel is located at a depth of m from the surface groud. The tuel has got cross sectio is circular with the tuel s radius R= 3.15 m, the tuel liig is made reiforced cocrete. The desig parameters of the tuel liig are listed below: - Youg s modulus E l = 355 MPa; - Poisso s ratio ν l =.15; - Liig thickess t l =.3 m. Based o the data collected from the above studies, some characteristics of the strogest earthquakes that ca occur i the Haoi area are [1]: - Earthquake with a imum M W of 6.5; - Distace from the epiceter of the earthquake to Haoi is to 5 km ad peak groud acceleratio a =. g. 151

2 Iteratioal Joural of GEOMATE, Ja., 18 Vol.14, Issue 41, pp Table 1 Parameters of layers soil i Haoi ceter [1] Number of soil layers Elastic module, E, MPa Poisso s ratio, µ Thickess of layer (h), m Depths of soil layers, m Desity of the soil, ρ, g/cm Groud water level, m CALCULATION METHOD 3.1 Wag s Method [3] I 1993, Wag based o closed form solutios recommeded by Peck et al, proposed modified aalytical equatios i terms of axial force, bedig momets ad displacemets uder exteral loadig coditios. Wag may be the first perso i the world give equatios that be used to calculatio structural forces i the tuel liig uder seismic loadig coditios. I case full slip at the soil liig tuel s, bedig momet M ad forces ormal T ca be writte by Wag: 3 E(1 ν ) R F = 6 EJ(1 + ν ) E G = (1 + ν ) (7) (8) I 13, Kouretzis el al proposed a equatio of the imum bedig momet i liig tuel uder o slip coditio whe effect dyamic loadig, this to improve the Wag s method. R M = ± ( K K ) τ (9) K E π T = ± K Rγ cos ( θ (1 + ν ) 4 1 E π M = ± K Rγ cos ( θ (1 + ν ) 4 1(1 ν ) Where K = 1 F + 5 6ν (1) () (3) I case o-slip at the soil the liig tuel, oly the ormal forces T ca be expressed by Wag [1993]: 1 E π T = ± K Rγ cos ( θ + (4) (1 + ν ) 4 Where 1 F[ (1 ν) (1 ν) C] (1 ν) + K = 1+ 5 F[ (3 ν) (1 ν) C] + + C 8ν + 6ν + 6 8ν (5) E( 1 ν ) R s C = (6) Et (1 + ν)(1 ν) τ = ± V ρ G (1) Where τ - the imum free field seismic shear stress, ρ - desity of the surroud groud, G - the imum groud shear modulus, V - the peak seismic velocity due to shear wave propagatio. (1 ν)(1 C) F.5(1 ν) C+ K = (3 ν) + (1 ν)c +.5(5 6 ν) (1 ν)c + (6 8 ν) K 4 [ ] F [ ] [ ν ] [ ν ] [ ] F [ ] (11) 1 + (1 ) C F.5(1 ) C = (3 ν) + (1 ν)c +.5(5 6 ν) (1 ν)c + (6 8 ν) (1) Where K 1 - full-slip liig respose coefficiet; K - o-slip liig respose coefficiet; F - flexibility ratio of tuel liig respectively; E s - Youg s modulus of tuel liig respectively; C - compressibility ratio of tuel liig respectively; ν s - Poisso s ratio of tuel liig respectively; R - tuel radius respectively; J s - iertia momet of tuel liig per uit legth of the tuel (per uit width); t - thickess of tuel liig respectively; ν 15

3 Iteratioal Joural of GEOMATE, Ja., 18 Vol.14, Issue 41, pp Poisso s ratio of groud mass surroudig tuel; E - Youg s modulus of groud mass surroudig tuel; G - shear modulus of groud mass surroudig tuel; I - momet of iertia of the liig tuel; γ - imum free-field shear strai; θ - agle measured couter-clockwise from sprig lie o the right. 3. Pezie s Method [4] Pezie & Wu (1998) ad Pezie () developed similar aalytical solutios for the thrust momet ad shear i tuel liig. I case full-slip coditio at the soil-liig, the ormal forces T ad bedig momet M, that be defied by equatios: 1EI d π T = cos ( θ + ) d (1 ) 4 s liig 3 ν 6EI d π M = cos ( θ + ) d (1 ) 4 s liig ν 4EI d π V = si ( θ + ) d (1 ) 4 s liig 3 ν liig free field (13) (14) (15) ± d = ± R d (16) R 4(1 ν ) = ± α + 1 (17) 3.3 HRM Method [5, 6, 7, 8, 9, 1] The HRM method has bee give by Duddeck ad Erdma [1985], Takao [], Oreste [7], ITA [1988], AFTE [1997b]. This method is part of the umerical methods category ad simulates the iteractio betwee the liig tuel ad eviromet material surroudig the tuel by a umber of idepedet Wikler type sprigs. Whe usig the HRM method must the defiitio of the active loads that apply directly to the liig tuel structure. Mashimo ad Ishimura [3] preseted differet methods that be used to calculatio these loads. I case of havig effect of seismic loadig, ecessary to estimate the active loads o the tuel liig. Peize ad Wu [1998] ad Naggar et al. [8] preseted equatios, these ca be used to calculatio of ovalig deformatio of a circular tuel durig a seismic due to the i plae shear stresses caused by vertically propagatig (otice that, i case of the seismic load o the tuel liig, all the exteral loads are rotated couterclockwise by 45 ad the horizotal loads are i opposite directios). I this study, Matlab program was used to calculatio for the iteral forces o tuel liig by HRM method. σ h k s σ v k R EJ, EA σ h 1 EI(5 6 ν ) α = dg(1 ) s 3 ν (19) I the case of o-slip coditio, the formulatios are preseted as: ± = ± = () liig free field d R d R γ 4EI d s liig π T = cos ( θ + ) 3 d (1 ν ) 4 6EI d s liig π M = cos ( θ + ) d (1 ν ) 4 4(1 ν ) R = ± α EI(3 4 ν ) s α = 3 dg(1 ν ) d (1) () (3) (4) σ Fig. Calculatio scheme of tuel liig with the HRM method. σ v: vertical load i the model tuel surroudig groud; σ h: horizotal load i the model tuel surroudig groud; k : ormal stiffess of the iteractio sprigs; k s: tagetial stiffess of the iteractio sprigs; R: tuel radius; EJ ad EA: bedig ad ormal stiffess of the tuel liig. 3.4 D umerical model v I case have seismic load, umerical models have recetly bee used more ad more to model bored tuels liig. With the umerical models, that ca be possible to build tuel models ad material eviromets surroudig the tuel with the close most atural parameters. I this study, the umerical model is built by meas of the fiite differece elemet program Abaqus (imulia Corp). The soil eviromet surroudig the tuel 153

4 Iteratioal Joural of GEOMATE, Ja., 18 Vol.14, Issue 41, pp behavior has bee assumed to be govered by a elastic perfectly - plastic costitutive model, based o the Mohr-Coulomb failure criterio. The tuel liig behave liearly ad elastically. The umerical aalysis has bee performed uder regardless of the effect of gravity ad groudwater coditios. A time history aalysis has carried out usig data of El Cetro earthquake (with characteristics of the El Cetro earthquake almost idetical to characteristics of the strogest earthquake that ca occur i the Haoi) M w = 6.5 richter ad be showed i fig. 3 [11]. All methods be caculatio for case o-slip at the soil liig tuel s Time, s Fig.3 Data i El Cetro earthquake Acceleratio, g I the D umerical model, soil layers are replaced with a sigle soil layer with equivalet properties [1]: - Youg s modulus, E = MPa; - Poisso s ratio, =.34; - Dampig ratio is 5%. The D umerical model is 18 m wide i the x- directio, 8 m i the z-directio. Phases of the costructio process of tuel i this study: - Phase 1 (model setup): This is the first step correspods to the setup of the model, assigmet of the plae strai boudary coditios, there is o reflectio wave at the boudary of model ad do t takig ito cosideratio the ifluece of the gravity ad groudwater. The model was divided two parts, part 1 cotais the tuel ad the soil layer surroudig the tuel, the secod part is the area usig ifiite elemets so that the model has ot wave reflectio pheomeo. (Figure 4, 5); - Phase : Costructio of the tuel, iclude built parameters of soil layer ad liig tuel, assigig the liig tuel's with layer soil lik coditios (assumptios the cotiuous tuel liig without joits). ettig up the pressure over the whole tuel boudary o both tuel structure ad model's boudary, assig to the peak groud acceleratio of the earthquake to the model (see Figure 5); - Phase 3: The results obtaied after ruig the model (see Figures 1, 11, 1) Fig.4 Geometry problem of the D umerical method Abaqus software 154

5 Iteratioal Joural of GEOMATE, Ja., 18 Vol.14, Issue 41, pp Fig.5 Tuel model uder cosideratio 4. REULT AND DICUION I table, aalysis results be preseted. The iteral forces i liig tuel (the bedig momet ad ormal force) obtaied from HRM method be preseted i Figure 6, 7. Wag s method, Pezie &Wu s method i Figures 8, 9 ad D model umerical i Figures 1, 11, 1. Bedig Momet M (knm/m) Bedig Momet M (knm/m) No slip - Pezie & Wu No slip- Wag" -15 θ (degree) θ (degree) Fig.6 Bedig Momet M i the liig tuel by HRM method Normal force T (kn/m) θ (degree) Fig.7 Normal force T i the liig tuel by HRM method Fig.8 Bedig Momet M i the liig tuel by Wag s method ad Pezie & Wu s method Normal force T (kn/m) No slip - Pezie & Wu No slip - Wag θ (degree) Fig.9 Normal force T i the liig tuel by Wag s method ad Pezie & Wu s method 155

6 Iteratioal Joural of GEOMATE, Ja., 18 Vol.14, Issue 41, pp Fig.1 Result calculatio of model tuel s by D umerical method Fig.11 tate stress o the tuel liig i D umerical method Fig.1 trai of the tuel liig i D umerical method 156

7 Iteratioal Joural of GEOMATE, Ja., 18 Vol.14, Issue 41, pp The iteral forces i liig tuel Table ummary of aalysis results Wag s method Pezie & Wu s method HRM method D umerical method M (kn.m/m) T (kn/m) σ (MPa) Note: tress limit of tuel liig, [ σ ] limit = MPa Results i Table 3 show that all stresses o the liig tuel, which were calculated by aalytical methods ad umerical methods, are less tha the limited stress values of the tuel liig s material ad the imum stress obtaied i 3 aalytical methods are higher tha that obtaied with the D umerical method. This could be attributed to the fact that, i the umerical model, the direct ifluece of the soil eviromet surroudig the tuel liig is cosidered. The D umerical model uses direct data from the earthquake, this is may be do results were received i higher accuracy tha the results of aalytical methods. Further, these are reasos that ca be explaied for these results: the soil layer surroudig tuel has bee assumed to be govered by a elastic perfectly-plastic costitutive model, based o the Mohr-Coulomb failure criterio ad had got impact of dampig ratio of soil ad tuel liig (dampig ratio is 5% i this paper). The presece of dampig ratio i the soil surroudig the tuel liig ad i the tuel liig reduced the impact of earthquakes o the liig. This dampig ratio is a mai reaso that was the vibratio of the layer soil surroudig tuel ad vibratio of tuel liig decrease a value over time, therefore, the iteral force o the tuel liig is reduced. These reasos reduce the iteral force that occurs i the liig. However, it should be oted, i results obtaied from the D umerical model, displacemet of the soil surroudig tuel ad tuel liig uder the effect of the earthquake about.1 cm. This displacemet ca make cracks, deformatio ad tuel istability develop, although the iteral force value by effect of earthquake i the tuel liig is smaller tha the durability of the tuel liig up a lot. 5. CONCLUION I this paper, a lot of methods calculatio about impact of earthquake to tuel liig were used. Results of iteral forces iduced i the tuel liig of Haoi metro system determied usig Wag s method, Pezie & Wu s method, HRM method ad D umerical model Abaqus software were preseted ad comparative. Uder the impact of the earthquake, that has got strogest magitude ca occur i the Haoi s area, the stress o the tuel liig of the Haoi metro system is smaller tha value of the stress limit of the tuel liig (σ <[ σ ] = MPa) ad ca be cocluded limit that the tuel liig (with selected characteristics) could operate safely uder the impact of earthquake waves. However, aalyses poited out some differeces i the iteral forces o the liig tuel, these are bedig momets ad ormal forces have bee determied by aalysis methods ad umerical method. There are quite large differeces i results of stress o the tuel liig betwee the aalytical methods ad the D umerical method. These are explaied by the reasos: 1. The D umerical method demostrates the itercoectio ad iteractios of soil surroudig the tuel ad liig;. The D umerical method has used the soil surroudig tuel as be a elastic perfectly-plastic costitutive model based o the Mohr-Coulomb failure criterio ad the tuel liig is liear elastic model (I aalysis methods were to cosider layer soil surroudig tuel ad the tuel liig as be elastic material model); 3. The D umerical method take ito accout the effect of the dampig, through the dampig ratio, i this study is 5%. Results received by have bee calculated usig aalytical methods ad D umerical methods usig the Abaqus software have cofirmed the safety of tuel i Haoi metro system uder the impact of earthquakes. However, it should be oted that i the results of the D umerical method there is a displacemet of the tuel ad the soil surroud the tuel, this displacemet may be does ot break the tuel liig but ca make cracks, deformatio of the tuel liig ad the tuel could be loosed qualities whe tuel be used. 6. ACKNOWLEDGEMENT This work was supported by the ait Petersburg Miig Uiversity. We would like to thak to our colleagues i the Departmet of Udergroud Costructio, Faculty of Costructio from Miig ait Petersburg Uiversity ad Haoi Uiversity Miig ad Geology for helpig with data collectio. We thak two aoymous reviewers for their commets that were very valuable for revisig the mauscript. 157

8 Iteratioal Joural of GEOMATE, Ja., 18 Vol.14, Issue 41, pp REFERENCE [1] Gospodarikov Alexadr, Thah Nguye Chi. Liquefactio possibility of soil layers durig earthquake i Haoi, Iteratioal Joural of GEOMATE, Vol. 13, Issue 39, 17, pp [] Ba qua ly du a duog sat Haoi., Thuyet mih du a tau die gam Haoi, Du a xay dug he thog tau die gam Haoi, Haoi, 13, pp [3] Wag J. N., (1993). eismic desig of tuels: A state of the art approach, Parsos Brikerhoff Quad & Douglas Ic., New York, NY, Moograph 7. [4] Pezie J., Wu, C,. tresses i liigs of bored tuels. Joural of Earthquake Eg. tructural Dyamics 7, 1998, pp [5] Ngoc Ah Do. Numerical aalyses of segmetal tuel liig uder static ad dyamic loads. PhD thesis, Lyo, 14, pp [6] Duddeck, H., & Erdma, J. O structural desig models for tuels i soft soil. Udergroud pace, 9(5-6), 1985, pp [7] Takao, Y. H. Guidelies for the desig of shield tuel liig. Tuelig ad Udergroud pace Techology, 15(3),, pp [8] Oreste, P. P. A umerical approach to the hyperstatic reactio method for the dimeshioig of tuel supports. Tuellig ad Udergroud space techology,, 7, pp [9] ITA. ITA guidelies for the desig of tuels. Tuellig ad Udergroud pace Techology, 3(3), 1988, pp [1] Mashimo,H.,& Ishimura, T. Evaluatio of the load o a shield tuel liig i gravel. Tuellig ad Udergroud pace Techology, 18, 3, pp [11] The outher Califoria Earthquake Data Ceter (CEDC). Data of El Cetro earthquake, [1] Gospodarikov Alexadr, Thah Nguye Chi. Accoutig for geological coditios ad characteristics of seismic waves i the area, where has tuel of Haoi metro system, Iteratioal coferece "cietific ad Methodical", IV, ait Petersburg, 17, pp Copyright It. J. of GEOMATE. All rights reserved, icludig the makig of copies uless permissio is obtaied from the copyright proprietors. 158