Groundwater Seepage Estimation into Amirkabir Tunnel Using Analytical Metods and DEM and SGR Metod Hadi Faradian, Homayoon Katibe Abstract In tis paper, groundwater seepage into Amirkabir tunnel as been estimated using analytical and numerical metods for 14 different sections of te tunnel. Site Groundwater Rating (SGR) metod also as been performed for qualitative and quantitative classification of te tunnel sections. Te obtained results of above mentioned metods were compared togeter. Te study sows reasonable accordance wit results of te all metods unless for two sections of tunnel. In tese two sections tere are some significant discrepancies between numerical and analytical results mainly originated from model geometry and ig overburden. SGR and te analytical and numerical calculations, confirm ig concentration of seepage inflow in fault zones. Maximum seepage flow into tunnel as been estimated 0.45 lit/sec/m using analytical metod and 0.68 lit/sec/m using numerical metod occured in crased zone. Based on SGR metod, six sections of 14 sections in Amirkabir tunnel axis are found to be in "No Risk" class tat is supported by te analytical and numerical seepage value of less tan 0.04 lit/sec/m. Keywords Water Seepage, Amirkabir Tunnel, Analytical Metod, DEM, SGR. I. INTRODUCTION ATER inflow into tunnels is one of te most important W problems in tunneling in rock media wic flows troug initial discontinuities and or wic is created in tunnel walls. Tis causes some matters in progress of tunneling suc as decrease in rock mass stability; make extra pressure on permanent and temporary stability system, destructive effects on geomecanical condition of rock and finally pysical and economical dangers appen. Due to impossibility of identifying and determining te wole factors wic are affecting water inflow into tunnels especially during drilling, anticipating te exact amount of seepage into tunnels in rock media is difficult. Terefore, analytical metods, due to application of some simplification and assumptions, mostly used to calculate seepage amount into tunnels. Some of te important investigations carried out in order to calculate water inflow into tunnels include [1]-[8]. In spite of analytical metods, wic are a total estimation of seepage, wit attention to basic equations of seepage flow and site caracteristics, wit applications of numerical H. Faradian is wit te Mining and Metallurgical Engineering Department, Amirkabir University of Tecnology (Teran Polytecnic), Teran, Iran (e-mail: Faradian@aut.ac.ir). H. Katibe is wit te assistant professor of Mining and Metallurgical Engineering Department, Amirkabir University of Tecnology (Teran Polytecnic), Teran, Iran (corresponding autor to provide pone: 0098 1645496; e-mail: Katibe@aut.ac.ir). metods suc as FEM, DFM, DEM, FVM water inflow into tunnel van be modeled and ten seepage into tunnel in various situations in site can be calculated. Tese metods in opponent to analytical metods are difficult in calculation. Also, tey require compreensive data about te site. Moreover, tere are less simplifications and assumptions in tese metods. Toug, numerical metods are very complex and application of tem is time consuming, owever, te results are more precision in comparison to Analytical metods [9]. In tis paper, water inflow into tunnel in some sections of Amirkabir Tunnel is anticipated. First, analytical metods are used in seepage calculation. After tat, according to boundary conditions and site caracteristics, seepage in rock media around te tunnel is calculated in UDEC software wic depends on te Different Element Metod. Ten, tese sections quantitatively and qualitatively in point of underground water inflow danger wit SGR metod are rated. Katibe and Aalianvari (009) provided SGR metod to rate tunnel lengt qualitatively and quantitatively in point of underground water seepage danger depends on initial site investigations [10]. According to te mentioned calculations in addition to seepage estimation into tunnel, accuracy and precision of results in comparison to te results of SGR metod are evaluated. II. INTRODUCTION TO ANALYTICAL EQUATIONS OF SEEPAGE INFLOW INTO TUNNELS AND THEIR VALIDATION RANGE REVIEW STAGE Analytical metods based on te equations of water inflow into tunnels wit respect to parameters suc as rock mass permeability, water table, tunnel radius, etc. estimate water infiltration into tunnels. Table I sows te analytical equations. In tese equations H 0, distance between tunnel center and water table, Z, overburden, r, tunnel radius, K, equivalent permeability coefficient of rock media along seepage flow, Q L, infiltration amount per unit. Fig. 1 sows an overview in relation to parameters used in te equations presented in Table I. Analytical equations under te following conditions are invalid [9]: 1. Water inflow around te tunnel is vertical.. Bedding in te rock mass around te tunnel is very variable. 3. Rock mass permeability cannot be exactly identified. 96
TABLE I ANALYTICAL EQUATIONS OF GROUNDWATER SEEPAGE FLOW INTO TUNNELS Equation Reference Equation Description Number Goodman (1965) [1] Freeze and Cerry (1979) [] Heuer (1995) [3] Lei (1999) [4] El-Tani (1999) [5] Karlsrud (001) [6] Lombardi (00) [7] El-Tani (003) [8] (1).3 () (3) (4) KHo Q H o ln( ) r KHo 1 QL z ln( ) 8 r Q K ln( ( ) 1) r r r 1 3( ) (5) Q K r r (6) (7) (8) [ 1 ( ) ]ln( ( ) r Q K ln( 1) r Q k r ln 1 0.4 r Q 1 k 1 ln Tis equation as tree basic defaults; radius flow, no significant canges in bedding, accurate application of media equivalent permeability. H is te ydraulic ead, te dept of te tunnel wit H. Tese researcers ave revised equation 1 by substituiting Z instead of H. Heuer reduction coefficient (1/8) and some canges in denominator applied in order to revise equation. In tis equation, Goodman metod as been corrected wit application of exact real conditions. El-Tani as defined equation 5 as an optimum equation by considering above mentioned equations. A combination of equation 1 and 3, according to field observations, is edited for reducing error in deep and sallow tunnels (under water table). In tis equation, Karlsrud metod as been corrected wit application of exact conditions. In tis equation El-Tani as applied Mobius transformation metod and fourier series and presented a new analytical solution for flow calculation, in wic 1/ ( / r) (( / r ) 1) Primarily, in analytical metods a tunnel is compared wit a vertical water pumping well under a steady state regime and te mentioned equations are inferred based on te simulation of conditions of pumping a well under a steady state regime or a tunnel wic is located in a considerable dept towards water table. Under tese conditions seepage into tunnel wells are assumed equal and symmetric (or to be more precise isotropic) in all directions. On te oter and, te most important factor in analytical metods is to determine te equivalent permeability of te media around te tunnel and due to inaccurate estimation of tis parameter, most of tese metods encounter wit problems during water inflow estimation. Permeability coefficient (K) is inferred from lugeon test done in boreoles in various dept and it is generalized into intervals between boreoles. In places were lugeon tests are not performed, wit attention to geological caracteristics and boreole conditions, equivalent permeability is estimated but it as many problems [1]: 1. In lugeon test, a small volume of rock mass is tested and te calculated permeability is assumed as an equivalent permeability of uge volume of rock masses.. Individual geological structures suc as faults, breccia and crused zones control fluid flow. However, it is possible tat none of tese structures are test in lugeon test. Toug te results will be differ from wat is fact. A uge volume of flow appens wen a rock mass wit ig permeability exists around te tunnel. Altoug, it is known tat tey form only a few percent of rock media surrounding tunnel. In tis case, ig permeability values interfere wit low permeability values. Terefore permeability value in a region will be affected by ig and low values. On te oter and, analytical metods by means of ydraulic analysis and regardless of existing discontinuities encounter wit problems in estimating te accurate groundwater inflow. In analytical analysis, interaction between flow and stress is avoided, owever, in nature te interaction between flow and stress affected. Fig. 1 Tunnel condition in Goodman equation and introduction of parameters Tunnel is in te saturated zone. (1) ground surface, () groundwater table wic is possible to be upper tan burden, (3) water motion zone wit equivalent permeability coefficient, K, (4) inner zone of tunnel [9] III. DISCRETE ELEMENT METHOD Discrete element metod based on block teory is developed in order to analysis discontinuous media. In tis metod, te mass of te object is intended as a collection of separate blocks. Also deformations and beavior of ingredients of te blocks are assumed negligible. Joints and cracks in te media are act as discontinuities between blocks or boundary conditions or assumed as a special element in te model. Tis tecnique depends entirely on making rock mass discontinuities ideal and makes simulation of complex relationsips of joints, cutting and separation, plus a lot of movements and turning blocks possible. Blocks can be rigid or flexible. Blocks are assumed impermeable in point of ydraulic view and flow passes troug te joints. In numerical metods, conditions are assumed closer to reality in wic te upper boundary of te model only as flow and lower and lateral boundaries ave no flow. Accordingly, leakage into te tunnel from roof will be more tan floor and side walls. Tis condition, according to relative proximity of tunnel roof to groundwater table (sortness of leakage pat) tan side walls and floor is more reasonable in terms of adaptation to natural condition. Te main difference between DEM and analytical values lies in tis fact [11]. In fact, due to difference between leakage condition into tunnel in isotropic analytical metod and anisotropic numerical metod, calculated values ave significant differences. On te 97
oter and, in numerical metods interaction between flow and stress and simultaneous ydromecanics process are taken into account wic in turn affects te flow witin te rock mass [11]. UDEC, a -D numerical analysis software based on discrete element metod used for modeling discontinuous media. Tis software is planned and produced in 1971 by Dr. Cundall accompanied by Itasca company in Pennsylvania, USA. UDEC model te response of discontinuous media (jointed rock mass) toward various static and dynamic pressures. Te model created in tis application consists of separate blocks in wic discontinuities are considered as boundary conditions between blocks. UDEC works based on algoritm calculation. UDEC software as capability of analysis fluid flow in fractures existing in a system of permeable blocks. Te analysis of tis relationsip is ydraulic-mecanical. Tis means tat ydraulic conductivity of joints depends on te mecanical deformation and vice versa joints water pressure affect mecanical calculations [1]. IV. TUNNELS SITE RATING IN POINT OF GROUNDWATER SEEPAGE HAZARD VIEW BASED ON SGR COEFFICIENT Katibe and Aalianvari proposed SGR rating system based on initial site investigations for te first time in 009 in order to classify tunnel lengt qualitatively and quantitatively in point of groundwater seepage azard view [10]. In tis rating system, wit taking into account parameters like frequency and aperture of joints, Scistosity, crased zones, karstification, soil permeability, water ead above tunnel, annual raining and score tem, tunnel lengt divide into 6 classes from groundwater leakage azard point of view: No Danger, Low Danger, Relatively,, Higly and Critical. According to tis metod, total score of site compute from: SGR ( S1 S S 3 S 4 ) S 5 S 6 S 7 were: S 1, score of frequency and aperture of joints, S, scistosity, S 3, crased zone, S 4, karstification, S 5, soil permeability, S 6, water ead above tunnel, S 7, annual raining. It is obvious tat in rocky site parameters like crased zone, joint frequency and karstification is more of importance in opposed to earten site. Vice versa, in earten site permeability coefficient is more important, wile, in rocky media tis factor is lies witin frequency and aperture of joints and etc. Toug, in rocky site S 5 and in earten site S 1 to S 4 are assumed zero. Annual raining becomes important wen a tunnel is drilled in an unsaturated zone. Wile, a tunnel is drilled in a saturated area, it is assumed as unit. After computing SGR coefficient for a considered section of a tunnel, tere must be a criterion to evaluate magnitude of te coefficient, so tat te azard of groundwater seepage into a tunnel (wit a qualitative and quantitative point of view) could be evaluated. Tis is proposed based on te values in Table II. Anticipating groundwater inflow into a tunnel leads to design a suitable drainage system and also selecting te (9) most appropriate drilling metod, so tat necessary arrangements are made to prevent probable dangers. Te larger te SGR coefficient is, te volume of infiltrated water will be ig (at least in sort term), so tat drainage systems must be stronger and igly cost. Even, sometimes revision in drilling metod must be done in order to reduce probability of dangers. TABLE II QUALITATIVELY AND QUANTITATIVELY RATING OF TUNNEL SITE FROM GROUNDWATER SEEPAGE POINT OF VIEW BASED ON SGR COEFFICIENT [10] Probable conditions for SGR Tunnel Rating Class groundwater inflow into tunnel (lit/s/m) 0-100 No danger I 0-0.04 100-300 Low danger II 0.04-0.1 300-500 Relatively III 0.1-0.16 500-700 IV 0.16-0.8 700-1000 Higly V Q>0.8 1000< Critical VI - V. CASE STUDY; AMIRKABIR TUNNEL Amirkabir tunnel located in nortwest of Teran is designed and performing to transfer water from Amirkabir dam to Teran. One of te problems will be occurred in tis project is te probability of water in rus into tunnel during drilling operation. In tis paper, te results of analytical, numerical metods and groundwater seepage rating (SGR) in 14 sections of Amirkabir tunnel (3.1-14.1 km) are investigated. A. Geology of te Area In geological studies wic ave been performed, tunnel divided into 14 geological units wic is generally encompasses various sedimentary-volcanic sets of Karaj formation. Its petrology contains layers of tuff, sandstone, fine-grained conglomerate, siltstones, lava and agglomerate. In tis study, te possibility of leakage from +3.1 km to +14.1 km of te tunnel lengt is considered wic is divided into 9 geological parts: Gta, sandstone layers, tuff, Gta3, sandstone layers, tuff, fine-grained conglomerate, Gta4-1, sandstone, tuff, Gta4-, tuff, in some parts sandstone and conglomerate, Sts1, tuff, siltstone, sandstone layers and micro-conglomerate, Sts-1, tuff, limestone, Sts-, tuff, limestone, siltstone, sandstone layers and conglomerate, Ts-1, sandstone, sale, siltstone, Cr, tuff, sandstone, micro-conglomerate [13]. B. Results of Analytical Metods As noted above, in analytical metods wit taking into account parameters suc as equivalent permeability of rock mass, water table eigt and tunnel radius, te rate of seepage into tunnel is estimated. Some conditions and assumptions sould be considered to apply tese equations [9]: 1. -D flow and circular tunnel section.. Homogenous and isotropic permeability 3. Tunnel section is located under water table (in saturated zone). Basically, water ingress rate into tunnel is presented in te form of discarge rate or more precisely, water inflow volume 98
per time per unit lengt of te tunnel. Due to sligt geological variations of media around boreoles and in te distance between two adjacent oles, te effective lengt around eac ole is defined in wic water table and permeability coefficient is assumed equal to te data of te ole. Seepage rate into tunnel in te mentioned lengt is determined from multiple of lengt to discarge rate. Water leakage rate into tunnel is computed based of te data of eac boreole by taking te above conditions and assumptions into consideration and provided in Table III. C. Results of DEM Metod (UDEC Software) In UDEC software, by importing boundary conditions (stable ead, steady state flow and or no flow boundaries), rock mass and joints caracteristics as well as teir geometry coordinate, as well as te situation of tunnel and its section, permeability and groundwater ead is computed in different points of a aqueous layer. Ten, terefore seepage rate into tunnel can be calculated. It is obvious tat te accuracy of calculations by software is totally depends on te accuracy of input parameters [13]. In order to anticipate leakage rate in some parts of te tunnel, DEM metod is applied. Because of tat discontinuous media is modeled wit UDEC software pack wic is based on discrete element metod and as te capability of modeling fluid flow in a system of impermeable blocks and investigates ydro-mecanical beavior of media. Te model is formed of a block wit 30 meters lengt, 30 meters eigt, two continuous joint set and a tunnel wit 4.7 diameter wic is located approximately in te center of te block. Fig. sows model geometry as well as boundary conditions. Required data for modeling sections are gatered from field information and investigations in initial investigations of Amirkabir tunnel. Water inflow rate into tunnel in 14 sections of tunnel lengts are provided in Table III. Fig. 3 sows water pressure in one of te modeled sections after tunneling and seepage. TABLE III RESULTS OF ANALYTICAL AND NUMERICAL METHODS; SEEPAGE RATE INTO TUNNEL IN 14 SECTIONS OF AMIRKABIR TUNNEL Section number Section situation (meter) Water discarge (lit/sec/m), Numerical metod, UDEC Water discarge (lit/sec/m), mean of analytical metods Relative difference (%) 1 3100 0.111 0.113 1.5 350 0.175 0.16 9.6 3 3800 0.686 0.45 61.4 4 400 0.181 0.184 5 4650 0.147 0.164 10.5 6 550 0.04 0.047 11.7 7 6700 0.03 0.09 8.8 8 7500 0.0 0.0 8.1 9 7900 0.487 0.456 6.9 10 8350 0.066 0.068 1.9 11 950 0.018 0.018 1.6 1 10800 0.031 0.05 0.3 13 1150 0.036 0.035 3.4 14 13550 0.011 0.038 7 Fig. Model geometry wit boundary conditions Fig. 3 Water pressure in a section of Amirkabir tunnel after tunneling and seepage D. Groundwater Seepage Hazard Rating and Inflow Anticipating wit SGR Metod By taking into account parameters suc as joints aperture, dept of tunneling, widt of crased zone, eigt of groundwater table above tunnel axis, SGR coefficient in 14 sections of tunnel lengt is computed. Te results are sown in Table IV. It is obvious tat because te site of Amirkabir tunnel is rocky, parameters like Fracture and joints, joints frequency and karstification ave more of importance. Toug, permeability coefficient is considered as zero and S 7 coefficient (related to annual raining score) is assumed as unit because te tunnel from 3.1 km to 14.1 km is drilled in saturated zone. Te results sow tat 6 sections from 14 sections is in No Danger class, sections in Low Danger, sections in Relatively, sections in and sections is in Higly dangerous and critical class. Wit respect to geological structure and rock types wic are mainly low permeable rocks, it can be claimed tat te major danger in tunneling is related to crased zones wic in SGR rating system, tey ave been rated as igly dangerous and critical class. As can be seen in Table IV, sections of crased zones, 3800 meters and 7900 meters, ave 1008 and 8984. SGR coefficient, respectively wic are rated in igly dangerous and critical class. Terefore, tese zones sould be igly considered in tunneling. 99
E. Result Analysis Because Amirkabir tunnel is drilled in jointed rocky media and Discrete element Numerical metod as capability of application in discontinuous media as well as simultaneous ydromecanics analysis, te results of water inflow estimation into tunnel in mentioned sections is more reliable in numerical metods tan analytical metods. Fig. 4 sows te results of analytical and numerical water inflow into Amirkabir tunnel calculations in 14 different sections. As can be seen, bot of te result sets ave similar pattern. Wit respect to Table III, te maximum seepage wic is computed by numerical metod is 0.686 lit/sec/m in section 3. Also in analytical metods, it is computed 0.45 lit/sec/m in te same section wic is occurred in crased zone. In oter words, bot analytical and numerical metods ave a similar variation pattern. But, relative difference of results in more tan 70 percent of sections is less tan 10 percent and in te oter ones, it is more tan tat. Te maximum relative difference of numerical and analytical results is in sections 3 and 14 wic are 7% and 61.4%, respectively. In section 14 in 13550 meters of te tunnel, te overburden and water ead is 65 and 490 meters, respectively. Stress of overburden and water pressure lead to a fine aperture of joint sets. So, due to simultaneous ydraulic process in discontinuities and interaction between flow and stresses of too overburden above tunnel, te amount of seepage modeled wit UDEC is negligible and relative difference between analytical and numerical metod is ig, approximately 7%. Also, in Section III in 3800 meters of tunnel lengt, te results of analytical and numerical metods sow a relative difference about 69% wic is due to geometry of te model. Because tis section is located in Gta crased zone, in order to compute groundwater seepage rate wit numerical metod and assuming igly dangerous seepage condition, te size of te smallest block in te section (lowest distance between discontinuities) is considered. So tat, te amount of groundwater ingressing into tunnel is estimated 0.686 lit/sec/m by means of numerical metod. Also, By SGR metod, tese sections are investigated in point of groundwater seepage azard view (wit qualitative and quantitative view). Fig. 5 compares te amount of seepage in 14 sections mentioned by numerical and analytical metods wit SGR proposed class for te flow rate. As it is said, eac class of SGR is quantitatively located in a special range of flow and in Amirkabir tunnel, proposed seepage ranges of SGR are in accordance wit te results of analytical and numerical metods. Based on SGR, Analytical and Numerical metods groundwater seepage into tunnel is concentrated in crased zones. Based on SGR, 6 sections of 14 sections in Amirkabir tunnel lengt is in No Danger class wic is in accordance wit te results of analytical and numerical metods wic sow a flow less tan 0.04 lit/sec/m. As can be seen in Fig. 5, all groundwater inflow amounts computed wit analytical and numerical metods are in te SGR proposed range. Also, seepage rate and SGR coefficient ave a similar pattern. TABLE IV RATING AMIRKABIR TUNNEL SITE IN POINT OF GROUNDWATER SEEPAGE HAZARD VIEW BASED ON SGR COEFFICIENT IN 14 VARIOUS ENGINEERING GEOLOGICAL SECTIONS Section (meter) S 1 S S 3 S 4 S 5 S 6 S 7 SGR SGR rating 3100 18.88 0 0 0 0 1.71 1 410 Relatively 350 16.60 0 0 0 0 30.73 1 510 3800 9.00 0 00 0 0 43.79 1 1008 Higly and critical 400 14.50 0 0 0 0 47.49 1 689 4650 11.64 0 0 0 0 4.9 1 49 Relatively 550 9.58 0 0 0 0 4.4 1 3 Low Danger 6700 0.0 0 0 0 0 45.8 1 1 No Danger 7500 0.00 0 0 0 0 15.57 1 0.004 No Danger 7900 0.11 0 300 0 0 9.94 1 8984.173 Higly and critical 8350 0.04 0 5.40 0 0 34.66 1 188.646 Low Danger 950 0.00 0 0 0 0 7.5 1 0.038 No Danger 10800 0.01 0 0 0 0 39.7 1 0.301 No Danger 1150 0.03 0 0 0 0 7.9 1.071 No Danger 13550 0.06 0 0 0 0 79.1 1 4.450 No Danger Fig. 4 Results of analytical and numerical groundwater seepage calculations into Amirkabir tunnel in 14 different sections. Values in te above of te columns sow te relative difference between te seepage results of analytical and numerical metods Fig. 5 Analytical, Numerical results and SGR coefficient in 14 sections of Amirkabir tunnel lengt VI. CONCLUSION 1. Te canges of groundwater seepage computed by analytical and numerical metods are te same in an acceptable limit. Just in two sections, Analytical and Numerical seepage values ave significant differences wic are due to model geometry and ig overburden. 300
. Tunnel site rating by SGR metod as a reasonable accordance wit values of analytical and numerical metods. Based on SGR metod and Analytical and Numerical calculations, seepage into tunnel is concentrated in crased zone. Maximum groundwater seepage by means of analytical metods is approximately 0.45 lit/sec/m and by application of DEM numerical metod, it is calculated about 0.68 lit/sec/m wic is occurred in crased zone of tunnel. Based on SGR metod, 6 sections from 14 sections of Amirkabir tunnel lengt is in No Danger class wit a flow less tan 0.04 lit/sec/m wic ave an accordance wit results of analytical and numerical equations. REFERENCES [1] Goodman, RE, Moye, DG, Scalkwyk, AV, Javandel, I, (1965) Groundwater inflows during tunnel driving. Bull. Ass. Eng. Geologists, pp. 35 56. [] Freeze RA, Cerry JA, (1979) Groundwater: Prentice-Hall, Englewood Cliffs, New Jersey. [3] Heuer RE (1995) Estimating rock-tunnel water inflow. In Proceeding of te Rapid Excavation and Tunneling Conference. Ed. G. E. Williamson and I. M. Growring; pp. 41-60. [4] Lei S (1999) An analytical solution for steady flow into a tunnel. Ground Water 37, pp. 3 6. [5] El Tani M (1999) Water inflow into tunnels. Proceedings of te World Tunnel Congress ITA- ITES 1999, Oslo, pp. 61 70, Balkema. [6] Karlsrud K (001) Water control wen tunneling under urban areas in te Olso region. NFF publication, 001. 1(4): pp. 7-33 [7] Lombardi G (00) Private communication. [8] El Tani M (003) Circular tunnel in a semi-infinite aquifer. Tunn. Undergr. Space Tecnol. 18 (1), pp. 49-55. [9] Faradian H, Aalianvari A, Katibe H, (01) Optimization of Analytical Equations of Groundwater Seepage into Tunnels: A Case Study of Amirkabir Tunnel. J. Geo. Soc. India 80, pp. 96-100. [10] Katibe H, Aalianvari A (009) Development of a new metod for tunnel site rating from groundwater azard point of view. J. App. Sci. 9, pp. 1496-150. [11] Jing I, Hudson JA (00) Numerical metods in Roc Mecanics. International journal of rock mecanincs and mining science, vol. 39, pp. 409-47. [1] Itasca (004) UDEC manuals, Minneapolis: Itasca Consulting group Inc. [13] SCE Company (006) Geological and Engineering Geological Report for Amirkabir Water Conveyance Tunnel Project (Lot1), unpublised report. 301