NUMERICAL MODELING OF HORIZONTAL PIT DRAIN DRAINAGE I N AN OPEN SLOPE by SHEMIN GE B. A. S c . , WUHAN I N S T I T U T E OF B U I L D I N G MATERIALS, CHINA, 1982 A THESIS THE SUBMITTED I N PARTIAL REQUIREMENTS MASTER F U L F I L M E N T OF FOR THE DEGREE OF OF A P P L I E D SCIENCE in THE The Department We of FACULTY Mining accept to THE OF GRADUATE and Mineral this the thesis required UNIVERSITY as STUDIES Processing conforming standard O F BRITI^tKcOLUMBIA April,1985 © Shemin Ge, Engineering April,1985 ^ In presenting requirements of British it freely agree for this for an available that in partial advanced degree Columbia, I agree for understood that financial by his or the shall reference and study. I extensive her shall copying of granted by the not be allowed of make further this thesis head of representatives. publication the University Library copying or gain at of the s c h o l a r l y p u r p o s e s may b e or fulfilment that permission for department for thesis It this my is thesis without my written permission. Department W '^'^W ho^^ of The U n i v e r s i t y o f B r i t i s h 1956 Main M a l l Vancouver, Canada V6T 1Y3 Date DE-6 (3/81) £ ^ Columbia >JK~ ft ^f^J^J ABSTRACT A study horizontal open pit drainage A has drain system, to slopes. Water computer model length INTRODUCTION 1982). flow was TO the were between hydraulic length. to in computer used that their Therefore, was and height the effects fanned drain element computer zone was field were as show vs. length were of different of of such was of mining the from a design drain made to rock rock of and as an system. study the slopes. The conditions mining slopes on is progresses. drain rows A comparison of patterns, made. series spacing operation simulation. also from relationship s p a c i n g between drain The Anderson, a drain also feature computer rock taken & drain anisotropic by layouts, (Wang horizontal vertical in was assumed. data simulations, the model obtained. graphs in in drain obtained the MODELING influence varies data Columbia and Another suitable investigated drainage the effect. studied. saturated the of a horizontal drains simulations indicated of of drawdown into s p a c i n g and results table effects were distribution characteristics drainage by the flow These drainage the water computer head the water spacing, agreements of evaluate parameters the British c o u l d be determine The the plotted. They the GROUNDWATER result graphs aid in to finite tested Satisfactory As and simulate LORNEX M i n e on Two m a j o r dimensional constructed the made drainage slopes. two been parallel the drain TABLE OF C O N T E N T S Page ii ABSTRACT TABLE OF C O N T E N T S LIST OF F I G U R E S LIST OF T A B L E S iii v viii ACKNOWLEDGEMENT ix Chapter 1. INTRODUCTION 1 Chapter 2. MATHEMATICAL MODELING 6 2.1 The Physical 2.2 The Mathematicl 2.3 Finite 2.4 Chapter 3. Chapter Element 9 Solution 13 Computer 20 Program and V e r i f i c a t i o n COMPUTER A N A L Y S I S Horizontal 3.2 Vertical 3.3 Anisotropy 3.4 The Model Model 28 Analysis Comparision 28 Analysis Effects of ..47 on D r a i n a g e Different 56 Drain Layouts ...58 Applications 4.1 Hypothetical 4.2 The 5. Problem 13 15 18 3.1 4. 7 Basic Theory F i n i t e Element Formulation Boundary C o n d i t i o n s Pattern Chapter Problem 65 Example Application for 65 LORNEX M i n e SUMMARY AND C O N C L U S I O N S 72 77 5.1 Conclusions 77 5.2 Summary 78 iii T A B L E OF CONTENTS (continued) Page BIBLIOGRAPHY 80 Appendix A. Finite Element Appendix B. Computer Formulation Program Organization iv 83 89 LIST OF F I G U R E S Figure Page 1. A Horizontal Drain Drainage 2. Hypothetical Slope with 3. The 4. A s s o c i a t e d Nodes 5. Boundary Condition 6. The View LORNEX Open Pit 7. M o d e l S e c t i o n o f LORNEX M i n e Conductivity Distribution and 8. The Data 9. Water Plan Table of Comparison of of Finite 2 Drains Position and System in Two . Sections 8 of a Elements Applied Computer Mesh .10 16 19 24 the Output Hydraulic 25 and the Field LORNEX M i n e Element Slope 26 for Horizontal Model 29 10. D i m e n s i o n l e s s H y d r a u l i c Head D i s t r i b u t i o n for t h e S l o p e H e i g h t o f 150m, D r a i n L e n g t h 90m 32 11. D i m e n s i o n l e s s H y d r a u l i c Head D i s t r i b u t i o n for t h e S l o p e H e i g h t o f 150m, D r a i n L e n g t h 80m 33 D i m e n s i o n l e s s H y d r a u l i c Head D i s t r i b u t i o n for t h e S l o p e H e i g h t o f 150m, D r a i n L e n g t h 70m 34 D i m e n s i o n l e s s H y d r a u l i c Head D i s t r i b u t i o n for t h e S l o p e H e i g h t o f 150m, D r a i n L e n g t h 60m 35 D i m e n s i o n l e s s H y d r a u l i c Head D i s t r i b u t i o n for t h e S l o p e H e i g h t o f 150m, D r a i n L e n g t h 50m 36 D i m e n s i o n l e s s H y d r a u l i c Head D i s t r i b u t i o n for t h e S l o p e H e i g h t o f 175m, D r a i n L e n g t h 100m 37 D i m e n s i o n l e s s H y d r a u l i c Head D i s t r i b u t i o n for t h e S l o p e H e i g h t o f 175m, D r a i n L e n g t h 90m 38 D i m e n s i o n l e s s H y d r a u l i c Head D i s t r i b u t i o n for t h e S l o p e H e i g h t o f 175m, D r a i n L e n g t h 80m 39 D i m e n s i o n l e s s H y d r a u l i c Head D i s t r i b u t i o n for t h e S l o p e H e i g h t o f 175m, D r a i n L e n g t h 70m 40 D i m e n s i o n l e s s H y d r a u l i c Head D i s t r i b u t i o n for t h e S l o p e H e i g h t o f 175m, D r a i n L e n g t h 60m 41 12. 13. 14. 15. 16. 17. 18. 19. v L I S T OF F I G U R E S ("continued) Figure 20. 21. 22. 23. 24. Page D i m e n s i o n l e s s H y d r a u l i c Head D i s t r i b u t i o n for t h e S l o p e H e i g h t o f 2 0 0 m , D r a i n L e n g t h 100m 42 D i m e n s i o n l e s s H y d r a u l i c Head D i s t r i b u t i o n for t h e S l o p e H e i g h t o f 2 0 0 m , D r a i n L e n g t h 90m 43 D i m e n s i o n l e s s H y d r a u l i c Head D i s t r i b u t i o n for t h e S l o p e H e i g h t o f 2 0 0 m , D r a i n L e n g t h 80m 44 D i m e n s i o n l e s s H y d r a u l i c Head D i s t r i b u t i o n for t h e S l o p e H e i g h t o f 2 0 0 m , D r a i n L e n g t h 70m 45 Dimensionless Hydraulic the Slope Height 60m 46 Water Table Position in a Slope 100m H e i g h t 50 27. Water Table Position in a Slope 120m Height 51 28. Water Table Position in a Slope 140m Height ........52 29. Water Table Position in a Slope 160m Height 53 30. Water Table Position in a Slope 180m Height 54 31. Water Table Position in a Slope 200m H e i g h t 55 32. The Effects of Anisotropic Materials 33. Parallel 34. Finite 35. The Comparison of Fanned and P a t t e r n s , S l o p e H e i g h t 150m Parallel The C o m p a r i s o n of Fanned and P a t t e r n s , S l o p e H e i g h t 175m Parallel The Comparison of Fanned and P a t t e r n s , S l o p e H e i g h t 200m Parallel 37. 38. The Fanned Drain Element Slope Vertical Length 26. and for Drain for Finite Drainage Mesh 200m, Distribution 25. 36. Element of Head Mesh Section of for the vi a Model 48 Patterns Fanned Drain 57 59 Pattern 60 Drain 62 Drain 63 Example Drain 64 66 L I S T OF F I G U R E S ("continued) Figure 39. 40. A . 1. Page Estimated Slope Water Estimated Water The Table Position in the Sample 70 Global Table Matrix Position Assembly in from LORNEX M i n e Individual Elements B . 1. Flow Chart B.2. An E x a m p l e 75 88 for to the Show Computer the Program Computer vii FESHDMS Input Data 91 98 LIST Tables • I. The Comparison II. III. IV. Calculation Example of Two TABLES Sets of Result Table Table Page 27 68 Calculation Calculation OF Table for LORNEX M i n e v i i i 69 74 ACKNOWLEDGEMENT I would Brawner this for like his research I to continuous guidance appreciate W. Poling A. J . Reed and D r . would Rulon and proven to also faculty Professor and encouragement C. 0. during comments H. J . L. like D. D. S. my c o m m i t t e e Miller. Smith to of for thank am g r a t e f u l helpful Dr. Goldman. The I members; A. Dr. to Dr. advice. R. Freeze, discussions with Dr. J . them have encouragement from valuable. Discussions the the and D r . Dr. be to program. G. I e x p r e s s my t h a n k s with members and graduate staff and Mineral Processing from Xu Changyu and Lu N i n g students, in the Engineering, in Department and China are the all of Mining encouragement appreciated. 1 Chapter 1 INTRODUCTION Groundwater open pit greatly that of mine water rock, stress, other in To the systems in conditions, cost trenches Among and to easy long systems. with a slopes install, A recent vacuum has with horizontal drain The in a to develops shear blasting seepage to is strength increases due in slope mechanism shear cracks movement , is or forces reduce slope many are development shown under its equipment are low in vacuum. cost system is geologic availability (CANMET, They need 1980) has are little compared some quick upkeep, to other horizontal drains advantages material. shown drain drainage drainage combining great drainage galleries, gravity, lower horizontal drain conductivity drainage several circumstances. by to different drainage horizontal work are to They drains in necessary There according and lower it slope. wells, others life slope. induced concerns table effective pressure factors. methods, over major water requirements, horizontal advantages be of the practice pumping these provide in effective and the stability drainage drainage, the the 1983) slope table used water of tension may direction improve water in shock (Brawner, of reduces pressure and one A high stability pressure vibrations, stability. and the water are stability. hydrodynamic acting the slope reduces the conditions in in draining A Figure typical 1. 2 Figure 1.- A Horizontal Drain Drainage System 3 (Seegmiller, In the design been done or a drain the which thesis 2. 3. the slopes with To estimate of drains as to work the is drainage system. less emphasis During design for embankments of these the the design in are the only to use the for horizontal primarily with this presented study open p i t in on respectively drain methods of drain commonly b a s e d attempting dealt research of testing. knowledge, their on rigorous even horizontal author's the no and T e s a r i k ( 1 9 8 4 ) difference some mining ways slopes such slope materials the as the and the slopes. the objectives hydraulic the the the the in this head horizontal different investigate on situ finite four after spacing in are determination and of level materials and and a n i s o t r o p y To e s t i m a t e To The studies from are drain published was height There length embankments, heterogeneity 1. To differ varying aspect. related there particularly, and e r r o r d e s i g n . While of horizontal Williams(1982) element design in as trial previously finite literature, mining, this study embankments. two in years published a In such experience two for 1982) parameters past geotechnical guides (Williams, has 1979) lengths suitable pit the on drains installed and are the drain in spacings. distance between rows deeper. influence drainage distribution vertical extends study. of results. anisotropy of slope 4 4. To compare layouts, To two fanned achieve followed. a the v a l i d i t y LORNEX by Mine the of and is finite the performances for a different drain The design pattern is In the r e l i a b i l i t y study practice of is parameters develop a experiences the computer presented a selection of provide for design. shows great thesis model f i r s t , drain basic More the potential organization, in Chapter and 2. in this the not The form. a simple depends of in on the good of this the drain order to drain design. and field research description model with heights. intention technique third spacings, and horizontal simulation development is needed the drainage slope evaluation is The graphical system The from and a verify system parameters research for in the INTRODUCTION drainage varying in to the information engineers. a computer and flow 1982). lengths drain geologic to book, were simulates data simulate results of field the drain layouts horizontal experienced the to drain interpret methodology Combining In to of task. judgement of water & Anderson, horizontal combinations step (Wang which Second, with from program different final model drain procedures model method. taken different four saturated element MODELING of patterns. computer state, example use The a computer to drain objectives, steady an results p a r a l l e l develop the GROUNDWATER step and to dimensional slope drainage these F i r s t , rock TO the area. of the verification are computer simulations 5 which involve the simulation are presented the computer analysis interpretation in Chapter 4 to study. Chapter 5 contains details of the finite program are presented in are show the on in different Chapter the summary 3. models Two application and formulation Appendix A and B, examples of conclusions. element and and this The computer respectively. 6 Chapter 2 MATHEMATICAL MODEL Groundwater in mining slopes i s represented by the flow of f l u i d through porous media. E a r l i e r research in this area of fluid flow through porous media was based on a n a l y t i c a l methods. These developed mathematical for methods, treatment of originally, problems of were heat flow, e l e c t r i c i t y and magnetic f i e l d s . With the development of the digital computer and i t s widespread a v a i l a b i l i t y , many of the important recent advances in the analysis of groundwater systems have been based on much d i f f e r e n t mathematical approaches generally known as numerical methods. The element method is finite one of the numerical methods. It i s the most widely used in research work and i s employed in this study. (Freeze & Cherry, 1979) To solve involves groundwater four steps. The problems first by step numerical is methods to examine the physical problem encountered in practice. The second replace the physical problem by an equivalent mathematical problem, which, in more s p e c i f i c terms, i s refered to boundary i s to value as a problem. The t h i r d i s to solve the boundary value problem for unknowns by computer techniques. The f i n a l step i s to interpret the numerical solution in terms of the physical problem. The emphasis of this study was the final step. placed on The d e t a i l s of that part, therefore, were arranged in a separate chapter while the other three parts 7 are included 2.1 The in Physical The 2, in open section To and simulate water different open on drain level water BF, pressure most significance EG is from determined assumed not the of toe flow to the by be on were the would is be same drain the plane, the slope toe the groundwater by zero drains(CD and water flows out region along these drains. the drainage. AH in not pressure between two compared along 2) this for considered left along under horizontal hydraulic The Figure only level conditions pressure obtain information the that to therefore, EG was horizontal comprise highest boundary has in on midway right and problem the The slope a so as is providing regional the and likely drains, which the in affected of into interesting lines slope in materials. line(BF) has enough will performed parallel far show problem illustrated pit analyses other analysis. As on the the common distribution with be slope Particularly Along stability the a drainage. an anisotropic along is of conditions, distribution drains. slope The the study section pressure sections. under pit dimensions. heterogeneous the problem a vertical horizontal three chapter. Problem physical encountered Figure this are AC, to head on and is boundary it. a As is the installed, but also 8 Free Surface after Drainage Free Surface before Drainage H drain (a). Vertical section (b). Horizontal section Figure 2.-Hypothetical Slope with Drains 9 To estimate the varying heights of case it model 2.2 is more which is dimensional element shown However, which could drains in for a a computer program large storage result in a slope three mesh section is construction due often to very the cost the and three results for Therefore, section, computer phreatic two two another on subject that surface dimensional of computer codes a vertical much number of indicated dimensional finite requires large high embankments three requires for same a dimensional design of two produced locations models, section, one were study. horizontal in the model evaluated analytically (Murray,1973). are phreatic validity In does vertical The the this (a). element assumption. of In vertical drain this assumption the on on a h o r i z o n t a l component on rows, considered. (Tesarik,1984) drains. The 2 be drain study the in The and Tesarik's dimensional used the time. unknowns must work Figure problem. time between to into computer nearly slope between Problem model, horizontal in distance flowing considerable run. the convenient Mathematical Water vertical include direction. of this by general, achieved surface not is the for the This the results situations relatively is assumption Murray best water flat. and using where flow the Dupuit has been Monkmeyer the the Dupuit slope drain » t w 1 IT i 1 i 1 A — (a). Plan View H-w-f- (b). S e c t i o n A - A h-"—H (c). Section B - B Figure 3 . - W a t e r Table Position along S l o p e 11 In a vertical blanket mining (b), used in the level, the a 3 a intersection of the ignoring the results the flow of of any on Using w steady both state flow . two reached materials can be smaller w could with in to the are water Figure the 3 drains, into the slope the toe drain length. It than actual be plane the drains back and the in see the as real the reaches and the by finding the the vertical model is estimated on vertical dimensional drain model and section, the is slightly 1982) and no d r a i n a g e after modelled. Heterogeneitic from model estimated equation flow zone. case, table along surface always of further spacing is treated not drains, distance water is height is is individual two surface the drain section horizontal horizontal were the specific w the at completed The perpendicular conditions are In the water 3, between , w conservative.(willams, In Figure drain that In in water which simulation level. which midway (b), at see length. dimensions, maximum. function to the drainage. the Figure is obvious drain slope point simulation, A s shown (c), In three section be 3 slope. in the would Figure to in practice. usually table drain section and modelled. vertical was and used. at This the was when in the that water steady state drain assumed anisotropic modelling, means stage horizontal Flow section installation the properties saturated of slope 12 The medium steady is derived state governed from by the Darcy's Law (Freeze & Cherry, 1979; Where: x are and y flow and y h is and the Ky a r e Q(x,y) is the the dimensional equation continuity Supplement each saturated which of was water 4-1, in other, hydraulic directions, hydraulic two coordinates to the a following CANMET, perpendicular Kx in flow. 1976) two directions [L] conductivities in x and [L/T] head flow as unknown, influx into [L] or out of the region, [L/T] The analytical hydraulic and head Q(x,y). impossible as In due to region. To obtain method, boundary the governing problem is on a equation presented. uniquely, The next x, y, flow i.e., step Ky, solution be of to a (1) high boundary the is The of in the by known. to is set points be the Kx, conditions. problem and be region, equation from (1) would would necessary different problem of number of (1) analytical hand, certain are of boundary solution usually an shape other conditions The the the values are describe cases, irregular on conditions flow the equation function complicated solution, head of the and hydraulic of complicated most heterogeneity, numerical a solution any These problem. conditions mathematical to solve the 13 mathematical heads 2.3 in problem the Finite by the are are having medium. the simple more powerful and the commonly finite shapes and addition, a the the of hydraulic water the in The method are finite flow method without varying be in used a to solve homogeneuous other they two hand, are becoming methods with the has more method having complicated with solve element a numerical Compared great With method materials can are element element regions heterogeneous table methods finite modeling. element Analytical restrictions. computer, area. the obtained the above solve be can can to the difficulty shape ease. In problem because during the solution. Theory The solution types with flexibility processing Basic handle finite moving this only on digital method, can deal for used solution conditions the groundwater difference and boundary difference in It in being some c a s e s . without the tool used advantages. with of finite in exact methods, solutions development The complicated Numerical approximate of method mathematically problems solution approaches problems. analytical the Solution several value obtain region. Element There boundary study and of variation of a principle partial boundary in mathematics differential conditions is equation identical to states with that the certain minimizing the 14 functional which is found by a certain mathematical procedure. For the boundary this p a r t i a l conditions section, the differential associated function is equation which found are as discussed I. and the later in (1) (Remson,1971) I=/X[^Kx(||)2+lKy(||) +Qh]dxdy (2) 2 Where: R is the According for (1) head i.e. is function h(x,y) discrete the on the the areas triangular The region study. principle, equivalent which such could method is satisfies continous region elements. or The rectangular heads divided find minimize solve the the equation hydraulic functional I, R. which or to to that region hydraulic is is element h the be under variation head h(x,y) finite find nodes. the should satisfied procedure, be to hydraulic The to region at into an approximate equation is divided shapes of associated these nodes N elements nodes, 3hi method (3). into a In this number the elements with three are unknowns. with used or M unknown of can four If head 15 over the whole region requires i = 1 ,M on every each unknown node, therefore, procedures. solving Finite Element divide and in step region into the formulate following the illustrated number of unknowns solution the small be one equation formed could be into the equation more in accurate equations Figure elements, finite by for certain obtained by specified process. each element subregions. 31 -0 3h, As could be corporating in subregions, the the would Procedure first the There M equations equations conditions The node. Consequently, the boundary head the for i=1,M 4, a of these method The smaller results. each is to the Then, to node. on R node is associated elements all with a contribute to 31 the value number of of •g^r* nodes contribution to element the obtained. in The Similarily, all (usually of region, derivation its the an element 3 or 4), surrounding following procedure is is s u r r o u n d e d by the element nodes. equations detailed in For a has each could be Appendix 16 Figure 4. —Associated Nodes and Elements 17 (1). for triangular elements, rai ^ (2). for e K1 1 K12 K1 a 31 ' 3h, K2 K 2 K2 31 ^3h,J K , 2 ^3 3 rectangular ah, 31 3h, 1 2 K3 3 elements, K 1 K 2 1 i K 3 <hi c (4) 1 C 1 f K 1 2 1 3 K, „ 3 K2 o K2 K 2 2 r -\ h, Ct h, C 1 \ < 31 3h, 31 L U Kg31i K32 K„ , K« 9h Where: superscript [k] is the e and f element function of K:3« ^33 ft h, ft C 1 v- J R«-3 2 represent the stiffness material (5) element number, matrix, which propertities and is a element geometry {h} is the hydraulic {c} is the force boundary As step vector (4) is and to {C}. (5) conditions which each element, global stiffness labeling and (Wang & Anderson, strictly element 1982). Appendix The A. function element assemble a done a and for was unknown is formed This in vector, vector, were node •i l l u s t r a t e d head in labeling process of of geometry matrix the [K] and terms of of element the assembly next the geometry, is mesh. also 18 The result resulting from of the assembly t h e number of i s a set of sets of global equations. [K]{H}+{C}=0 Where: [K] i s the global {h} is the region, {C} The obtain h obtain force is the solution given to be i n c o r p o r a t e d the boundary boundary on the whole vector to solve Known H e a d Figure in solving types equation (6) to applied of (6) a l l boundary and t o conditions the equations. Figure in the simulation. boundary 5, pressure conditions toe of BG, HI, ML, are at drain This the s l o p e . At these positions,hydraulic to elevation hydraulic regional shows There their to a selected toe head of the values groundwater also positions is zero. the 5 have are involved. head according satisfy Boundary: the equal of equation conditions, conditions different from vector unknown remaining the In head Conditions To 1. hydraulic matrix values. Boundary three (6) stiffness i s the global problem equations heads datum. slope, which which f o r HM, t h e are heads a r e determined D E , JK are considered therefore, a r e assumably conditions applies at the determined and keep far specified by constant. the 19 Free Surface after Drainage (a). Vertical section (b). Horizontal section Figure 5.—Boundary Conditions Applied 20 2. Known F l o w AF, IJ, and having flow 3. the Rate are flow pattern. BD i s free are zero. ease. in difficult a the and be A. An was was applied to solution, were elevation tolerance. If not, estimated from the new solution p r o c e s s was are obtained (Desai, 2.4 Computer Programming The equations The Horizontal solve the Drain head repeated the surface equations {c} the using inflow formula condition is more was used then flow boundary if satisfied of crosses approach hydraulic position on flow adding of global see No a no equations. heads along they the until a free calculated After the equal within in free their specified surface previously satisfied was and results 1972). were computer type the to by the boundary: solving vector estimated, hydraulic the the iterative being a in of boundaries. surface heads boundaries symmetry boundary. third investigated heads of the these handled to The surface the free pressure was of cross incorporated free obtaining Method. the 2 with. 2, type element Appendix deal flows third 1 can of to condition surface the impermeable because 1 and Condition contribution (A-10) rate of surface Condition imaginary No w a t e r Combination the which LK zero Curve with Boundary: and Program s o l v e d by program, Drainage Finite in Verification the Gaussian Element Mining Elimination Simulation Slopes, FESHDMS, of was 21 written by Terminal System) B r i t i s h Columbia. described the in horizontal author at The The this and presented Appendix verify simulation. of is a 1. In The slopes sufficient a l l the Unversity the vertical computer data of computations the and numerical result or program output are there evaluate are solution be the of to physics a methods checked is computer the whether several could modeling of understanding to are practical Laboratory models which heterogeneity. construct Field if The (Michigan solution to verify by not easily interest. Its available for a p p l i c a b i l i t y is limited. Physical The any the our solutions of Physical 3. MTS in either of on Solution Analytical 2. do input in of cases, numerical problems of run B. Normally, Analytical could details procedure is IV Center for example many reasonable. very program v a l i d i t y groundwater model. an important the Computing The organization One FORTRAN chapter model. in in a the method data are d i f f i c u l t usually Also are much laboratory Measured model Model can are employed to build to simulate charaterized equipment may by be rock their needed to model. Data be tested available in this against and study. the f i e l d reliable. measured This is data the 22 The f i e l d obtained from Columbia. data the In used LORNEX this investigations were done and Most groundwater the Report C. producer the section major west wall as a was 6 which slope is intensive LORNEX staff providing was was British hydraulical with Golder specialist summarized section, check the can a advice. in Golder seen has been of competent, with section the and the computer due to data The some The faults. "*" slightly Figure the were in the data were used difference made 8 output. relatively assumptions to Figure computer the rock moderately simulation. and that and data in conductivity marked These 8 p i t . line major #35. Figure AB two as was vertical and Report measured A the open measured the pressure weathered points obtained. understandable modeling. view along were from recorded been i n s t a b i l i t y . heads of has the plan of Columbia Groundwater of molybdenum B r i t i s h p i t . wall from comparison mine west number Golder the copper of the slope At in Granodiorite results consistency on hydraulic from be cause of the the the comprised the available of pit central instablity major Bethsaida open the the shows easily by verification Highland Vally, some large shows distributions. It model the information a selected Figure shows in Brawner in The considered altered is located province. 7 0. the #35. LORNEX M i n e on Mine mine Associates of in in good is the 23 In addition, example (Wang taken from & Anderson, book, Chapter computer output as in shown It verified can by the computer model INTRODUCTION 1982). The 6 was is compared Table be the data put into with was TO in tested by an GROUNDWATER M O D E L I N G the the the also example computer result of in model, the this the example I. concluded field that data the with computer satisfactory model has results. been Golder Figure 6. The Plan View of LORNEX Mine Associates K12345- C o n d u c t i v i t y [m/s] - K = 3 E - 8 6 - -- K = 3 E - 8 -K=2E-8 7 -- K = 2 E - 8 -K=9E-9 8 -- K = 2 E - 8 -K=2E-8 9 --K=2E-6 - K = 7 E - 6 1 0 -- - K = 7 E - 6 Figure 7.-The Model Section on the West Wall of Lornex Mine and the Conductivity Distribution "1 0 I I I I I I I I 50 100 150 200 250 300 350 400 Depth f r o m 4752ft • I 450 1 500 1 550 Bench(ft) Legend O Measured Values X C o m p u t e d Values Figure 8.—The C o m p a r i s o n of C o m p u t e d and M e a s u r e d Hydraulic Head Values in LORNEX Mine 27 TABLE I. The Comparison of Node Number Two S e t s of Computer Outputs H y d r a ii l i c Head V a l u e s ( m ) Wang & A n d e r s o n FESHDMS 1 4.000 4.00 2 4.000 4.00 3 4.000 4.00 4 4.000 4.00 5 3.720 3.72 6 3.695 3.69 7 3.688 3.68 8 3.686 3.68 9 3.392 3.40 10 3.366 3.37 1 1 3.357 3.36 12 3.354 3.35 13 3.000 3.08 14 3.000 3.00 15 3.000 3.00 16 3.000 3.00 28 Chapter COMPUTER After the verified, Chapter it model was drains is 2. horizontal and between drain The and length simulations sections for anisotropic in the has the the the also included drainage materials in have effects of The vertical in distances it the should horizontal into on the the different both horizontal 2.2, taken modeling for on section vertical modeling, performance and in performed section been the specified lengths. section drains and horizontal suitable As d i s c u s s e d vertical were The and established problem drainage spacings of been simulations estimate rows. that model sections. analyze used to SIMULATIONS solve vertical different was noted to computer used to with spacing used The section be computer 3 account. horizontal slope drain with pattern layouts. 3.1 Simulations The was to purpose analyze system with head was on of the the the different The applied chapter, Figure element in mesh for on the this effects level section have 2. on s p a c i n g s and model conditions Section simulation drainage distributions studied. Horizontal (b) model been and is of horizontal the horizontal lengths. where and presented Figure shown in The drains geometry 5 sections in hydraulic are installed the boundary the (b). Figure drain The 9. previous finite Drain 50 40 30 20 10 I 0 1 1 1 1 I 1 40 1 1 — I — 1 — — 80 1 1 — I — ' — ' — ' — I — • — — 120 160 1 1 — I — 1 — • — 200 1 — I — 1 — — 24 0 1 1 — I — 1 — • — ' — I — ' — ' — ' 280 320 I X(m) Figure 9 . - F i n i t e Element Mesh for Horizontal Model • ' 360 ' I ' ' 400 ' I 440 30 In Figure represented by coordinates be in zero range lengths y The drain made can variable from under seen y. In spacings head for be all three upper 100m. the the by 80m by varying and lower A total slope of of is varying the to can 10m. the The length boundaries. 120 The computer drain heights, spacing spacings from combinations different drain different modelled the 50m t o the simulation range were on that the direction, lengths pressure lengths were it the modelled. different of 9, runs spacings 150m, 175m, and and 200m. The values computer at section. a The simulation number of hydraulic outputs separated heads on the drains are most important They interpreted into a Figure for 10 a slope slope is of of The a 14 175m, 15 Figure on the midway between to 20 the Figure to two analysis. dimensionless of head horizontal stability results Figure and of hydraulic plots. simulations 19 Figure for 24 the for the simulations for 200m. slope to be results significant impractical heights. slopes can the nodes for series show 150m, obviously 150m simulation of of of possible number is height height It range Figure height slope all to the line parallel were are which 200m. done of In need For any to do mining to be the practice, drained particular a fall into problem, great the the specifically. these reduction simulations of indicated hydraulic head in that a slope there from 31 no drains variations to in drain results. Within from slope the significant. less influence even very spacing a distance toe, the Beyond on the sparsely induced of that the 1.0-1.5 differences distance, hydraulic head spaced different times in drain drains. the drainage drain hydraulic length head s p a c i n g s have distribution. The is much 32 X/L h-Woter Table Height at Distance x H-Slope Height L-Distance from Toe to Headwater Drain Length l=90m ot depth 150m Figure 10. D i m e n s i o n l e s s H y d r a u l i c Head D i s t r i b u t i o n for t h e S l o p e H e i g h t o f 1 5 0 m , d r a i n L e n g t h 90m h-Water Table Height at Distance x H-Slope Height L—Distance from Toe to Headwater Drain Length l=80m at depth 150m Figure D i m e n s i o n l e s s H y d r a u l i c Head D i s t r i b u t i o n for t h e S l o p e H e i g h t o f 150m, d r a i n L e n g t h 80m 34 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 X/L h-Water Table Height at Distance x H—Slope Height L—Distance from Toe to Headwater Drain Length l=70m qt depth 150m Figure 12. D i m e n s i o n l e s s H y d r a u l i c Head D i s t r i b u t i o n for t h e S l o p e H e i g h t o f 150m, d r a i n L e n g t h 70m 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 X/L h—Water Table Height at Distance x H-Slope Height L—Distance from Toe to Headwater Drain Length l=60m at depth 150m Figure 13. D i m e n s i o n l e s s H y d r a u l i c Head D i s t r i b u t i o n for t h e S l o p e H e i g h t o f 1 5 0 m , d r a i n L e n g t h 60m 36 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 X/L h-Water Table Height at Distance x H-Slppe Height L-Distance from Toe to Headwater Drain Length l=50m at depth 150m Figure 14. D i m e n s i o n l e s s H y d r a u l i c Head D i s t r i b u t i o n for t h e S l o p e H e i g h t o f 1 5 0 m , d r a i n L e n g t h 50m 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 X/L h—Water Table Height at Distance x H-Slope Height L-Distance from Toe to Headwater Drain Length l=100m at depth 175m Figure 15. D i m e n s i o n l e s s H y d r a u l i c Head D i s t r i b u t i o n for t h e S l o p e H e i g h t o f 1 7 5 m , d r a i n L e n g t h 100m 1 h—Water Table Height at Distance x H-Slope Height L—Distance from Toe to Headwater Drain Length l=90m at depth 175m Figure 16. D i m e n s i o n l e s s H y d r a u l i c Head D i s t r i b u t i o n for t h e S l o p e H e i g h t o f 1 7 5 m , d r a i n L e n g t h 90m 39 \ X/L h-Water Table Height at Distance x H-Slope Height L—Distance from Toe to Headwater Drain Length 1=8Om at depth 175m Figure 17. D i m e n s i o n l e s s H y d r a u l i c Head D i s t r i b u t i o n for t h e S l o p e H e i g h t o f 1 7 5 m , d r a i n L e n g t h 80m 40 X/L h—Water Table Height at Distance x H-Slope Height L-Distance from Toe to Headwater Drain Length l=70m at depth 175m Figure 18. D i m e n s i o n l e s s H y d r a u l i c Head D i s t r i b u t i o n for t h e S l o p e H e i g h t o f 1 7 5 m , d r a i n L e n g t h 70m 41 0 0.1 0.2 0.3 0.4 0.5 X/L 0.6 0.7 0.8 0.9 1 h-Water Table Height at Distance x H-Slope Height L-Distance from Toe to Headwater Drain Length l=60m at depth 175m Figure 19. D i m e n s i o n l e s s H y d r a u l i c Head D i s t r i b u t i o n for t h e S l o p e H e i g h t o f 1 7 5 m , d r a i n L e n g t h 60m h-Water Table Height at Distance x H-Slope Height L-Distance from Toe to Headwater Drain Length 1=10Om at depth 200m Figure 20. Dimensionless H y d r a u l i c Head D i s t r i b u t i o n for t h e S l o p e H e i g h t o f 2 0 0 m , d r a i n L e n g t h 100m 43 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 X/L h-Water Table Height at Distance x H-Slope Height L-Distance from Toe to Headwater Drain Length l=90m at depth 200m Figure 21. D i m e n s i o n l e s s H y d r a u l i c Head D i s t r i b u t i o n for t h e S l o p e H e i g h t o f 2 0 0 m , d r a i n L e n g t h 90m 1 44 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 X/L h-Water Table Height at Distance x H-Slope Height L-Distance from Toe to Headwater Drain Length l=80m at depth 200m Figure 22. D i m e n s i o n l e s s H y d r a u l i c Head D i s t r i b u t i o n for t h e S l o p e H e i g h t o f 2 0 0 m , d r a i n L e n g t h 80m 1 45 h-Water Table Height at Distance x H—Slope Height L-Distance from Toe to Headwater Drain Length l=70m at depth 200m Figure 23. D i m e n s i o n l e s s H y d r a u l i c Head D i s t r i b u t i o n for t h e S l o p e H e i g h t o f 2 0 0 m , d r a i n L e n g t h 70m 46 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 X/L h-Water Table Height at Distance x H-Slope Height L-Distance from Toe to Headwater Drain Length l=60m at depth 200m Figure 24. D i m e n s i o n l e s s H y d r a u l i c Head D i s t r i b u t i o n for t h e S l o p e H e i g h t o f 2 0 0 m , d r a i n L e n g t h 60m 47 3.2 Simulations The purpose model was drain levels. applied finite to of The element 25. installed the the section shown mesh for level in with pit goes deeper, the slope the second of drains row distances from 20m i.e., the at section at drains. was of 1 and about 0.6 it Similar section sections the drains which are slope face. The illustrated in assumed to of 100m. toe and The modelled row of to 200m. the at the drain installed. from horizontal higher, ranging drains which of were The model are with slope drain length w the vertical were 120m As be to the level, 1 is in the smaller simulations and length. no with of real assumption having is 5. was are Dupuit was Figure installed. surface the drains assumption section or of is sections the table drain the modeling the two estimated the to the water where was of and between conditions becomes h i g h e r second vertical distance height levels height from instead times modeling, middle the section than slope distance used vertical case, the The intersection w, the slope were 100m, (b) drains height drain installed is the two 3 the boundary section of between to the Figure row on vertical and this first simulation suitable been the Section computer model The at Vertical the estimate have Figure on a been flow across symmetric drains. made The Therefore, in for the the the section. section water there horizontal must is, vertical In this between two flow toward actually, 300-1 250- / 200- A / v§, 150100- 00 50 100 150 i 200 i 250 ' — r 300 h — ' '—i—' — i — — i — 11 350 400 450 500 550 X(m) Figure 25.-Finite Element Mesh for Vertical Model 1 600 49 some water flowing understandable would be lower simulations result in would A systems that away the be that was having a section head water modelled. values calculated outgoing slightly w=40m the hydraulic than which from in from flow is It the the is field computer ignored. The conservative. used, which represented the drainage two parallel the vertical of computer |=0.8-0.85 Where: S is the horizontal drains, 1 is The the were drain The each slope height the water table results of than drains can range, and maintain distance becomes higher seepage force unfavourable table and 40m to the stable the and pit saturated becoming for as the larger slope would zone floor 26 drains such condition. higher factors 60m saturated results Figure for on positions after distance range, the plotted. that above a distributions water the [L] as before vertical that head were suggested the length, obtained calculations. between [L] hydraulic section spacing a be Greater pit and a slope not zone to the Figure were under is in 31 for show installed. suitable The range condition. the Less first row of relatively high and than that under the extends larger. stability. slope vertical first row deeper, These the are From F i g u r e very 29, Figure 26.—Water Table Position in the Slope 51 Figure 27.-Water Table Position in the Slope 52 Figure 28.-Water Table Position in the Slope 53 Figure 29.—Water Table Position in the Slope •9 Figure 30.-Water Table Position in the Slope Figure 31.-Water Table Position in the Slope 56 30, and the 31, it slope can face. sufficient to Therefore, they Otherwise, Slope stability 3.3 the height Because anisotropy to meters 100 Material the water at the made certain usually of ratios of very are stage. or reducing good d r a i n a g e is of results. drained about an not zone. earlier length near half zone of the maximum. Analysis feature study rock an width it is saturated at drain insure Slope to of installed to table second l e v e l height discontinuities special characteristics the a or were be necessary face, a a the original slope is simulations of such requires of that drains need are Anisotropic range The increasing spacing slope seen drain drain behind be of in rock slopes, such s l o p e s . the influence materials on conductivities the in The of computer anisotropic drainage. two the A directions wide were assumed: ROC=0.001, Where: ROC i s Although with a 70m, spaced at the anisotropic in Figure 60m slope and materials can has be a Of 10, 100, made on one system having of 150m, the drainage computer simulation seen 1000 Conductivities, was height indicate It 1, drainage a The 0.1, Ratio drain slope. 32. the simulation horizontal quantitatively 0.01, that significant the and slope the the on model results result Ky length nature anisotropy influence Kx is of of of can the plotted the rock 57 h-Water Table Height at Distance x H-Slope Height L-Distance from Toe to Headwater Drain Length l=70m at depth 150m Drain Spacing S=60m Figure 32.—The Drainage Effect of Anisotropic Materials 58 drainage effects. parallel to drains ROC the is further a The value a moving time, under freezing in effects of was to made drain As of Figure slope. The element mesh Figure 34. the mesh is drain For shown levels in same for in drains order to the When the greater, with hydraulic head cross parallel 9, to more a often save are equipment particularly discontinuities the computer performance drainage simulation of a fanned layout. two boundary the very To e s t i m a t e number are Layouts easier, patterns, 33, 2.3, Figure were in and drain same section finite the drainage Figure the or Pattern collection drain parallel have Drain directions. the direction drainage. 2 change pattern water in of the conditions, and in order the smaller. fanned compare 5, an in perpendicular horizontal practice, different shown to Different different simulation i.e., ROC, of make layout length in drainage in oriented face, become much slope installed conductivity with Comparison In larger favorable change distribution 3.4 slope more reaches The sections used in the of over the same conditions applied fanned drain drains to drain layout, Chapter 2. two specified in sections. The pattern the is finite Assuming at 1. 150m with a drain length 60m and spacing 60m, 2. 175m with a drain length 80m and spacing 80m, 3. 200m w i t h a drain length 100m and spacing shown 100m. in element that the (a). Parallel Drain Pattern (b). Fanned Drain Pattern Figure 33.-Parallel and Fanned Drain Patterns £ / / 'V > > > i0 ) 0 2 4 0 8 0 12 0 16 0 2( X(m) 28,0 . 3:20 3(50 Drain Figure 34.-Finite Element Mesh for Fanned Drain Pattern )0 4( 4* 61 The - c o m p u t e r drain models material most symmetric and is the as At the These slope, a if results the difference hydraulic distance of favourable local it pattern, is the ends achieve the drainage local drains. geology layout can make the more cost be is as of drains effective. a yield in a of the pattern drain becomes length from are nearly the length of decided, slope induce within toe. for If a a the a the no fanned discontinuities, i.e., smaller s h o u l d be better that parallel layouts used that in spacing order to achieved by c i r c u m s t a n c e s where the drain to 35, drain oriented fanned toe fanned been the many the especially, equivalent Figure known a certain pattern from in central difference the has drains, However, system over different more for in conditions exist results good a models reduction, fanned used to drainage drain geological between two that in the of drains length recommended t h a t parallel of head such parallel the is from value that in it value slope, twice fanned drain head the indicate and and on plotted length highest heads number head results, drain into distance parallel drain these the hydraulic fanned assumed c o n d i t i o n s . Homogeneous s e c t i o n s were hydraulic back on hydraulic of as made considered. both twice Further toe, same. for highest about smaller. only distance the pattern. three By a n a l y z i n g the slope, the were important line 37. within under s l o p e was The 36, simulations pattern, drainage installation more the fanned performance and efficient and 62 1- O.h 1 O.Oh 7 Legend : Fanned _ parallel O.OOI0 0.1 0.2 0.3 0. 4 I 0.5 X/L 0.6 0.7 0.8 1— 0.9 h-Water Table Height at Distance x H—Slope Height L-Distance from Toe to Headwater Drain Length l=60m, Spacing s=60m, at depth 150m Figure 35. Comparison For the of Fanned Slope and Height Parallel of 150m Drain Patterns 63 0.1 X t t —> / / T f Tanned ,/ parallel J 02 0.1 0.4 03 05 06 X/L 07 i 0.8 i 0.9 1 h—Water Table Height at Distance x H—Slope Height L-Distance from Toe to Headwater Drain Length l=T0m, Spacing s=60m, at depth 175m Figure 36. Comparison For the of Fanned Slope and Height Parallel of 175m Drain Patterns * 0.1 } > J $ t 1 / i * 0.01 —' — t / _ 1 -t 1 r / 3 anned Parallel 0.1 02 03 04 05 06 07 l i 0.8 0.9 1 X/L h—Water Table Height at Distance x H—Slope Height L-Distance from Toe to Headwater Drain Length 1=80rri. Spacing s=60m, at depth 200m Figure 37. Comparison For the of Fanned Slope and Height Parallel of 200m Drain Patterns 65 Chapter 4 APPLICATIONS The practical aid for horizontal this chapter, LORNEX Mine estimating drainage 4.1 sample is the having this study The water example, in cross and to the 38. ideal Two table the is in to provide mining slopes. application illustrate spacing for head on right the slope the procedures drain the a to horizontal an In the procedures geometry is local the were determined boundary height. of climatic Second, are the for using system design c o n d i t i o n s are assumptions position and the horizontal section conditions to study for drain Example relatively Figure case and this system design presented length A Hypothetic this drain of system. For of a purpose slope is First, regional environment. kept for results a slope outlined. made. by the constant shown the initial groundwater The hydraulic and slope material in is equal to considered be h o m o g e n e o u s . If the slope heterogeneous, FESHDMS hydraulic following it is simulation head the material in suggested to to obtain distribution procedures. the a use actual the detail instead of mine computer is highly program and more realistic going through I H -x 500m F i g u r e 3 8 . - T h e S l o p e S e c t i o n of t h e E x a m p l e 67 (1) . To Assume a D r a i n Assuming l=70m, equipment, (2) . the the use section Table line from on the geology drain and installation the slope height. slope height Values selected to the two 10m t o l=70m 18 of between ranging local Figure intersection (3) . h/H length h=l75m, depending specified To O b t a i n For Length and obtain drain the h/H level drains for values and each along the the vertical drain spacing 80m. Calculation Insert the data Calculation obtained Table II. completing data underlined are others calculated were from step Table III for this inserted obtained in by is very into Table example. Table the (2) III II after The from simple the data step (2), equation h=(h/H)*H Where: (4) . To Plot and h a r e Water Plot the data pairs, which (5) . h/H To estimated the (x,h) water Select Selecting a a extent known water in table Table table Because this previous III. in the as Check steps. study, it the stability is not in by using Figure 39 the in s=80m Stability satisfies the slope shown corresponds to spacing which of from Positions S p a c i n g and requirements. the Table all Requirement slope analysis discussed stability is beyond here. TABLE I. Calculation Table X/L=0 05 x= h/H h (m) s 10 20 30 40 50 60 70 80 x/L=0. 075 x= h/H h x/L=0 1 x= h/H h x/L=0. 15 x= h/H h x/L=0. 2 x= h/H h x/L=0. 3 x= h/H h TABLE I I . Example C a l c u l a t i o n Table X/L=0. 05 x=25m (m) h/H h x/L=0. 075 x=37.5m h/H h x/L=0. 1 x=50m h/H h x/L=0. 15 x=75m h/H h 10 0.00 0.00 0.00 0.00 0.024 4.20 0.087 15.23 0.15 26.25 0.28 20 0.00 0.00 0.00 0.00 0.03 5.25 0.09 15.75 0.15 26.50 0.283 49.53 30 0.00 0.00 0.005 0.78 0.037 6.48 0.10 17.50 0. 155 27. 13 0.286 50.05 40 0.002 0.26 0.01 0.045 7.88 0.11 19.25 0.16 50 0.004 0.68 0.016 2.80 0.05 0.115 20. 13 0. 165 28.88 0.292 51.10 60 0.007 1 .23 0.022 3.85 0.058 10.15 0.12 70 0.01 1 .75 0.028 4.90 0.065 1 1 .38 0. 125 21 .88 0. 175 30.63 0.298 52. 15 80 0.015 2.63 0.035 6. 13 0.071 12.43 0.13 s 1 .66 8.75 L=500m, H=175m 21 .0 x/L=0.2 x=100m h/H h 0.17 22.75 0.18 28.0 x/L=0.3 x=150m h/H h 49.00 0.289 50.58 29.75 0.295 51 .63 31.5 0.30 52.50 70 Figure 39.—Estimated Wctre Table Position in the Exampls? 71 In this case, corresponding to a design for the equal to 70m a n d l=70m and satisfactory the analysis or to Other Other the table slope safety not options spacing, increase and If the then be a the water satisfy the are either back drain position primarily length table the and is at stability keeping to length analysis drain the go the at stability system would can is factor, s p a c i n g 80m. other to water l=70m, stability repeat step (5). Considerations considerations anisotropy account drainage s=80m reducing (2) the s=80m, shows requirement, . if to properties, make the such etc. final as are local needed to decision. heterogeneity, be taken into 72 4.2 The Application The It is real for appliable without problem the condition The the 8 this wall range, it depths The in effective The The to slope deep drains region. to not graphs the which ensure this are be in or would is of to could by is at other would ideal has been of I0" m/s 7 In to adit shallow would be 1983) the level. 4752ft moving. The 448ft(135m). boundary is estimated be far enough reach such not to effectively 5200ft from vertical to with adit slope is considered slope drainage the a The 9 the upper constant be I0~ m/s. be a installed level drainage of depressurize the kept range Associates, wall will conductivity Whereas (Golder the the ideal. section, mine 6 150m. west to the for drains 4752ft could produced. wall liklihood heads were the system toe consistent 10" m/s to charts this mass h y d r a u l i c that from discussed. of the the In range 100m on is far these is drainge. slope hydraulic is drains drain at from 1300ft(400m) the crest reduce Mine horizontal for are pit likely slope, that Pit The horizontal height distance the by horizontal bench 2. the the pit the extreme is usually information of an depressurized system. which Mine modification. mine Chapter with mines Pit guidance some this under in west I0" m/s, design general described in LORNEX O p e n in conditions LORNEX O p e n situation unlikely in to The where to be from a far 73 The same p r o c e d u r e s a s followed. The considered (1) . in specific each l=90m installation (2) . To O b t a i n For the h=135m, are values and drain (3) . Table (5) . to the vertical mine feasible mine. l=90m in for (Golder and which real mine section spacing ranging are drain Report #35) from the the slope situations line of between 10m t o slope two conditions to the height obtain drain drains h/H level for each 80m. Calculation Table Plot Water the the pairs, data which the Select Selecting analysis II. from step Results are shown water table estimated (x,h) water in Table table S p a c i n g and a spacing which In this Check reducing for the the (2) in the into Table to for the s=80m, spacing to 60m, the VI. system and using Figure 40 Requirement slope water the in by s=20m the safety 40m, slope shown Stability unsatisfactory drainage as satisfies case, corresponding shows an VI in corresponds to a requirements. position obtained Table Plotting design is this intersection Calculation To in 10 the data in which selected the To this were Values using Figure Insert (4) . h/H length the of 4.1 Length (300ft) the along section conditions equipment closest in step. To Assume a D r a i n Assuming outlined table slope stability at the stability factor. Further 20m, ' t h e primary suggests that the drains TABLE s (m) X / L = 0 05 x = 20m h h/H 10 0.000 20 III. Calculation Table for LORNEX Mine x / L = 0 . 075 x=30m h/H h x/L=0. 1 x = 40m h/H h x / L = 0 . 15 x=60m h/H h x/L=0. 2 x = 80m h h/H x/L=0.3 x=120m h/H 0 . 00 0.00 0.00 0.00 0 .00 0.00 0.00 0.002 0 .27 0.13 17.55 0.00 0 . 00 0.00 0.00 0.00 0 .00 0.00 0.00 0.01 1.35 0.13 17.55 30 0.00 0 . 00 0.00 0.00 0.00 0 .00 0.002 0.27 0.018 2 .43 0.14 18.9 40 0.00 0 . 00 0.00 0.00 0.000 0 .000 0.005 0.675 0.025 3 .375 0.14 18.9 50 0.00 0 . 00 0.001 0 . 135 0 . 0 0 2 0 .27 0.009 1.215 0.03 4 .05 0.15 20.25 60 0.00 0 . 00 0.001 0 . 135 0 . 0 0 2 0 .27 0.014 1 .89 0.04 5 .40 0.15 20.25 70 0.002 0 . 27 0.004 0.54 0.007 0 .945 0.02 2.70 0.048 6 .48 0.16 21 . 6 0 80 0.004 0 . 54 0.007 0.945 0.01 1.35 0.025 3.375 0.052 7 .02 0.16 21 . 6 0 L=400m, H=135m h F i g u r e 4 0 . — E s t i m a t e d W a t r e Table P o s i t i o n in L O R N E X Mine 76 have (6). l=90m, Other The Considerations geologic shows that parallel The range of information the to favourable the s=20m. hydraulic the factor slope for s p a c i n g c o u l d be vertical reported face a is of in drain the in Report the greater drainage increased 40m-60m a c c o r d i n g t o Golder conductivity such spacing in some is Therefore, areas. levels study direction which system. #35 c o u l d be results in in the section 3.2. In for conclusion, LORNEX M i n e drain in the the recommended h o r i z o n t a l upper west wall length=90m, horizontal vertical spacing spacing 20m-30m, 40m-60m. is: drain system 77 Chapter 5 C O N C L U S I O N S AND SUMMARY 5.1 Conclusions From program, (1) . the the There drain a (2) . computer following is a a slope hydraulic with spaced drain Different within in distance in this research made. head no d r a i n s reduction compared at to the having system. s p a c i n g s have the done c o n c l u s i o n s are significant level sparsely simulations different of 1.5 to drainage 2.0 effects times of the drain length. Beyond influence (3) . (4) . on A suitable of drains The in that reduction vertical is slope in rock spacing hydraulic distance to the has little head. install range slopes conductivity face system. If order 2 or of of drain of plays the 40m an second to row 60m. important role performance. Higher to in suggested anisotropy drainage distance, is more the distribution values in favourable ratio of Kx a direction for to such Ky h a s a a greater, the change in becomes smaller with further parallel drainage value in hydraulic change the head in the ratio. (5) . Fanned d r a i n s produce and different parallel results in drains the in slope region near drainage the slope 78 face The drain h y d r a u l i c head a f t e r the i n s t a l l a t i o n of fanned drainage drainage length i s higher within from benefits the the than for parallel d i s t a n c e about twice slope t o e . However drain of the d r a i n the practical and c o s t b e n e f i t s of fanned d r a i n s a r e u s u a l l y substantial. 5.2 Summary T h i s study comprises a s e r i e s of to drains, f o r h o r i z o n t a l and v e r t i c a l spacing of drainage c h a r a c t e r i s t i c s i n a n i s o t r o p i c rock the drainage e f f e c t s of d i f f e r e n t d r a i n p a t t e r n The two dimensional finite element developed and used i n the s i m u l a t i o n . The was simulations model h o r i z o n t a l d r a i n drainage i n an open p i t s l o p e . I t i n c l u d e s the analyses and computer verified by the f i e l d data slopes layouts. program computer was program from the LORNEX Mine. The procedures f o r using the r e s u l t s of the study are outlined in examples i n Chapter 4. S e v e r a l assumptions were made i n the study. (1) . Darcy's law i s v a l i d , (2) . Flows are i n two dimensional (3) . The graphic saturated fields. r e s u l t s a r e based on s i m u l a t i o n s i n homogeneous m a t e r i a l s . i 79 In the area of mining slopes, there studied i n the f u t u r e horizontal are as a an drain few system aspects extension of design for that should this be research program. 1. To take the the t r a n s i e n t 2. drainage time i n t o account by m o d e l i n g flow models, To m o d e l t h e d i r e c t i o n a l d i s c o n t i n u i t i e s o f i n more on detail. rock slope 80 BIBLIOGRAPHY Abramowitz, M. and Stegum, Functions Applied with Bise, C . J . and Drainage C O . , General Symposium, Byrne, Denver, Mining, P.M. and W a l t e r for Nonlinear Soil R.F. Soil and Freeze, Janzen, of SME o f of Mine AIME, Cherry, Mine Drainage 1979 Stability in 1982 of Stresses Series the 52, Deformations Department University Canada, 2nd No. and December Edition, Program of of British 1981 1978, Van Nostrand Ltd. J.T., J.A., Cliffs, Mathematical Hillslope May Mine SOILSTRESS-A Computer Engineering, Englewood Sons, Analysis Drainage, Slopes, 3, Analysis Christian, Inc. and Aided International Rock Volume Co. and in of Mechanics R.A. A.R., Bureau Engineering, Colorado, Mechanics, Geotechnical Freeze, First Vancouver, Reinhold(l5) C.S. Tables, 1964 on M i n e Engineering, Columbia, Desai, the Surface Civil Craig, of Stability Soil, C , Mining and Math National Computer Report C O . , in Graphs, 55, D. Mathematical 1984 Proceedings Brawner, R.L., Systems, September, Brawner, Series Washington, Scyoc, Handbook Formulas Math. Standard, I.A., P177-125, Methods McGraw-Hill, Groundwater, N. Models Hydrology Numerical J . , of (M.J. 1978 in 1979 Prentice-Hall, 1979 Hillslope Kirkby, Hydrology, Ed) John Wiley, 81 Ge, Shemin, Lecture CIVL 573, British Golder Notes 1984 of and GEOL Columbia, Holland, I. Report and Tapir, August Kolbein, The K.H., The and T.C., Pazin, Drains Div., Murray, W.A. Son, for Soil ASCE. and Slopes, November Marlon-Lambert, of Cir. J . , CANMET R e p o r t Remson, I., Methods Sons. Rulon, J . , the in P.L., Mine B.L., of Norway, Engineers, John of of the Horizontal Geotech. Eng. Hydraul. Div., G.M. of Jour. Sept. 1973 Computer Analysis Supplement December 1977 and M o l z , F . J . , Hydrology, 4-1, CANMET, Numerical John Wiley and 1971 Heterogeneous Seegmiller, for Validity Seepage, Development Univresity (LORNEX Method, Design Equation, Subsurface Inc., of 1977 77-30, Hornberger, W.S., Slope Manual, Groundwater Wall, Element Method Jour, E n g . , V91, Pit West University Choi, and Monkmeyer, Soc. University ,1945 Dupuit-Forchheimer Am. 1983; 1983 Finite Element Inc. M. the 342, 1969 Finite Wiley GEOL Canada the Technical Trondheim-Norway, Huebner, of 1983; 1984, Vancouver, #35, Bell, 562, 564, Associates, Drainability Mine), Kenney, GEOL of of Multiple Hillslopes, British Horizontal Dewatering, Seepage Ph.D Columbia, Mine Drainage, along Thesis, June Drains-Their Faces Use the 1984 in Open Pit P r o c e e d i n g s of the 82 First International Mine Draingae Symposium , D e n v e r , C o l o r a d o , May 1979, P268 S h a r p , J . C , L e y , G.M.M. a n d S a g e , R., P i t S l o p e M a n u a l C h a p t e r 4 G r o u n d w a t e r , CANMET, CANMET R e p o r t 77-13, November 1977, P240 S m i t h , I.M. P r o g r a m m i n g Application Inc., Sterrett, to t h e F i n i t e Element Method Geomechanics, With John W i l e y and Sons. 1982 R . J . and E d i l , T.B., G r o u n d - W a t e r and S t a b i l i t y o f a S l o p e , G o r u n d Flow System Water, 2 0 , 1982, P5-11 T e s a r i k , D.R. a n d K e a l y , C D . , E s t i m a t i n g H o r i z o n t a l Design by Methods, t h e F i n i t e Element and F i n i t e Bureau Investigations:8875, of Mines Drain Difference Report of 1984, U. S. D e p a r t m e n t of the Interior W i l l i a m s , R., B l o o m s b u r g , G. a n d W i n t e r , G., I n f l o w o f H o r i z o n t a l D r a i n s i n T a i l i n g s Embankments, A Research Contract Reoport, M i n e s , U. S. D e p a r t m e n t August Mining 1982, B u r e a u o f of I n t e r i o r Wang, H.F. a n d A n d e r s o n , M.P., I n t r o d u c t i o n t o G r o u n d w a t e r Modeling-Finite Methods, Difference and Finite Element W. H. Freeman a n d Co. San F r a n c i s c o , 1982, P288 Z i e n k i e w i c z , O.C, The F i n i t e E l e m e n t M e t h o d , M c G r a w - H i l l , New Y o r k , 1977, P787 3rd Edition, 83 APPENDIX A FINITE The principle discussed of the in Chapter 2. formulation process of know the that region The is ELEMENT FORMULATION finite The c o n t e n t equation water flow of (A-1) is (4) in method this a n d (5) in a g o v e r n e d by e q u a t i o n functional element was appendix (Freeze following so as t o condition obtain must be |£=0 or if the unknown region head nodes, the ^ =;; T [ K for (A-1), comprised (A-3) x(||)| K i the satisfied: (A-3) of N i s equivalent 9hf i.e. solution on R R is 1979) (A-2) 2 + I, 2 . We I: 2 minimize the saturated & Cherry, I=/;t5Kx(||) 4Ky(||) Qh]dxdy To is in Chapter two d i m e n s i o n a l (1): briefly subregions with M to: u (||) Ky(||)| (||) + K i = 1 ,M + Q f ]axay=0 7 (A-4) 84 Therefore, equations The M equations a r e M h y d r a u l i c head formulation subregions. and c a n be o b t a i n e d , solution of M values. o f (A-4) d e p e n d s Two t y p e s the of element on t h e shape shape of the were u s e d , t r i a n g u l a r rectangular. Formulation f o r T r i a n g u l a r Elements Y (I. 3(x ,y ) 3 3 2(x within each element, t h e h y d r a u l i c heads function the of t h e i r position, interpolation interpolation function. =(1 a r e assumed t o be a The generalized is called form of x,y a r e p o s i t i o n heads (A-5) 3 x y ){a} {a} i s g e n e r a l i z e d hydraulic 2 f u n c t i o n f o r the t r i a n g l e i s : 2 The ,y ) i . e . h=h(x,y), which h=a,+a x+a y where: 2 coordinates coordinates at three nodes of the t r i a n g l e should 85 satisfy (A-5), i.e. h The matrix 3 1 x, y, 1 x 2 y 2 1 x 3 y 3 a. (A-6) < form i s : (A-7) {h}=[B]{a} {a} i s found to be: {a} = [ B ] - 4 h } =[A]{h} Substituting (A-8) into h-(1 (A-8) (A-5): x y)[A]{h} =[N]{h} In (A-9), _ In _ . • equation needed to [N] is a function „\ (A-4), 9h ^ , be known. (A-9) of x, y, x 1 f y 9h ' 9 / 9 h \ 9 /9h\ ^ , ^ ( ^ ) , ^ ^ ) , A l l of the terms 1 x f 9h a could h 2 , . . y 2 , 9x 911^9^ 9y 9y 9x 9hf9x'"9x , y 3 are be d e r i v e d from 9x 9 ^ 9 ^ 9y 9y 9_,9hx 9N_ 3 i=1 , 3 (A-9): 9x x (A-10) 86 9hT" Substituting e t o node ^ into i s obtained Li Where: The i (A-10) Nl (A-4), from the contribution the following ] Ae i s t h e a r e a simplified form of +K element ]{h} Q N l } d x d y e. becomes: (|^T)=[k,i k ] l element formation: ay 97^ "oT^ *r Tr dr ? dT of k ; k i]{h}+{Cj} 2 (A-11) 3 H=Kx(fi)(|^)Ae Ky(fi)(Mi)Ae + Ci=//QiNi Ae dxdy i = 1 ,3 and j=1,3 kfj three and Ci could corner Formulation The be computed by k n o w i n g the coordinates of points. for Rectangular interpolation Elements function for rectangular elements h=a, + a x + a. y+a xy 2 3 t h e same procedures elements, equation (A-13) (|^-) = [ k , i (A-12) ( | Following is i s : d e s c r i b e d above for triangular obtained: k 21 k ; 3 k , i ] { h } + {Ci} (A-13) 87 Ci=;/QfNj Ae i=1,4 Assembly of finished, global has and j=1,4 the Global After the the the form Matrix formulation next equation dxdy step for individual elements i s t o a s s e m b l e them f o r the whole s y s t e m . The into global of way t o form each element node numbering process.(Wang a set of equations of: [K]{h}+[C]=0 The is the global i s done (A-14) equation strictly and element & Anderson, (A-14) i n terms numbering. 1982) from of Figure the the A-1 equation geometry, shows t h e Element contributions are computed, dispersed, and summed to form the global matrix Nodes Element No. e X X X X X X X X X e = 5 Figure e = 6 A.1.-The Global Individual Global matrix Matrix i j m 1 1 i 3 2 2 5 3 3 T 4 5 4 4 6 5 5 5 6 7 6 6 8 7 Assembly Elements from 89 APPENDIX B COMPUTER B.1 Introduction The computer Simulation in this hydraulic dimensional capability flow (Finite Element Drainage i n Mining Slopes), to water p r e s s u r e steady state determine the as w e l l as flow flow in a two field. of the program p e r m i t s t h e f o r the following t h e l o c a t i o n of t h e f r e e water open p i t 2. d i r e c t i o n of and s a t u r a t e d groundwater FESHDMS a p p e n d i x was d e v e l o p e d head d i s t r i b u t i o n , r a t e s and flow The program, f o rHorizontal Drain described 1. PROGRAM analysis of problems: surface f o r water flow i n slopes; hydraulic head d i s t r i b u t i o n on a v e r t i c a l or horizontal section; 3. flow The following r a t e s and d i r e c t i o n s i n t h e flow region. computer p r o g r a m p e r f o r m a n c e s a r e s u b j e c t e d t o the conditions: 1. Darcy's 2. material law i s v a l i d f o r flows; conductivities can be heterogeneous and anoisotropic; 3. flow The region i s confined finite a p p r o a c h was u s e d or unconfined. e l e m e n t method by t h e v a r i a t i o n a l i n the simulation. The r e g i o n of principle analysis 90 is divided of the the equations form into of a number finite with of d i s c r e t e element the hydraulic the equations elements. formulation heads The results i s a s e t of a s unknowns. The The (B-1) [K] i s the global {h} i s t h e unknown hydraulic {C} i s the column vector flow matrix i s given by: [K]{h}+{C}=0 where: linear stiffness matrix head vector associated with the flux derivation of equation (B-1) has been shown in presented in Appendix A . B.2 Computer Program Organization Flowchart A flowchart Figure B.1. A program listing f o r the computer certain c o u l d make amount the program is o f comment program contained details in the relatively straightforward. Subroutines MAIN the main routine intitiates storage global geometry and g l o b a l storage and a c t s as a general control flow space, reads variables, routing the allocates routine. 91 Start — r Read heading and geometry Set dimension Allocate storage i 1 Call NODEIN Call ELEMTIN Read more d a t a PA,WT, time period Call CONDUC Call ECHO Call BUILD Call ASSEMB Call SOLVER Call COMPA T Call TRIAN u Call QUADS 1 Call TRIAN *1 C A L L INITI Call QUADS Call BUILD Call ASSEMB Call SOLVER t =0 * yes IF H=• y Call i Call IF No PHOUT * COMPA H=y yes ? Call ? PLOUT NO | Call PHOUT Call PLOUT Stop Figure B.1 Flow Chart for the Computer Program FESHDMS 92 NODEIN This routine part i scomprised of reads individual two node i n t e r p o l a t e s m i s s i n g nodes and data input. The second portions. data The from checks errors first unit in 5, node p a r t c a l c u l a t e s t h e number o f unknowns. ELEMTIN T h i s s u b r o u t i n e reads i n d i v i d u a l element 5, checks f o r errors and d a t a from calculates unit t h e maximum bandwidth. CONDUC S u b r o u t i n e t o r e a d c o n d u c t i v i t i e s of m a t e r i a l s and specified known h y d r a u l i c read h e a d s f r o m u n i t 5. ECHO Subroutine to print to unit 6 a l l node, element and m a t e r i a l data f o r v e r i f i c a t i o n . INITI For t r a n s i e n t problems, condition this subroutine does initial computation. BUILD The main element subroutine to form element m a t r i x f o r each a n d s t o r e them f o r a s s e m b l i n g t h e g l o b a l matrix. T R I A N a n d QUADS C a l l e d by BUILD, t h e y c a l c u l a t e t h e e l e m e n t t r i a n g u l a r and r e c t a n g u l a r matrix f o r elements. ASSEMB Assembly individual element matrix into the global 93 equation. COMPA For free surface computed problems, t h i s h y d r a u l i c heads elevation on subroutine free compares t h e surface with their heads. PHOUT Subroutine to print out t h e h y d r a u l i c head and p r e s s u r e head a t t h e e n d o f c o m p u t a t i o n . PLOUT Subroutine to plot mesh a n d water An example presented the slope section, finite element table p o s i t i o n . of the computer a t t h e end o f t h i s input Appendix. and output is 94 Variable (according to their Name appearing Number of Listing sequence in the program) NNODE total NU toatal NELT total Number of ELemenTs NMAT total Number of different NTRNGS total Number of TRiaNGular NQUADS total Number of QUADilateral NB Bandwidth NHK Number PA Atomspheric Pressure WT unit of P1 the first P2 the second Period P3 the third DELT1 the time interval in first DELT2 the time interval in second drainage DELT3 the time interval in third ITIME Index MAXIT MAXimum I T e r a t i o n XELT(1,I) X coordinate of Ith node in a ELemenT XELT(2,I) Y coordinate of Ith node in a ELemenT ESM(4,4) Element Stiffness EVE(4) Element VEctor BM(2,4) inter Number of of Unknow Known H e a d WeighT of NODEs nodes MATerial types elements elements nodes water Period of Period TIME heads drainage of of drainage drainage drainage drainage period period period step variables times Matrix 95 CONX CONductivity in X direction CONY CONductivity in Y direction STOR STORage HIN INitial H Hydraulic MB Maximum BX(MB) X coordinate of corner points on boundary BY(MB) Y coordinate of corner points on boundary XMAX MAXimum X coordinate YMAX MAXimum Y coordinate TOL specified TOLerance KC Known Head Head Boundary head 4-known; MC coefficient Movable corner Condition 5-free points of each node,0-unknown; surface Condition of each node, 0-free to move; 1-fixed MESH 0-no KCE Known mesh p l o t flux required; Condition with no known flow boundary NSECT O-vertical NSTADY O-transient; flow model; of 1-mesh each boundary; Element, 1-element 1-horizontal 1-steady state plot model 0-element with known Computer Storage Array Variable Storage Allocation Diagram A(20000) Position in Array Size N1 = 1 X NNODE N2=N1+NNODE NNODE N3=N2+NNODE CONX NMAT N4=N3+NMAT CONY NMAT N5=N4+NMAT STOR NMAT N6=N+NMAT HIN NNODE N7=N6+NNODE H NNODE N8=N7+NNODE NNODE N9=N8+NNODE GVE NNODE N10=N9+NNODE GSM (NNODE) N11=N10+(NNODE) HK NHK Array Varable Storage IA(2000) Position in Array Size IN1 KC NNODE IN2=IN1+NNODE MC NNODE IN3=IN2+NNODE I TYPE NELT IN4=IN3+NELT I MAT NELT IN5=IN4+NELT JELT 4(NELT) IN6=IN5+4(NELT) NC NELT IN7=IN6+NELT KCE NELT Free node • Figure Fixed nixie B.2. An E x a m p l e to Show the Computer Input 1St1ng of WAND a t 21:47:31 on JAN 30. 1985 f o r CC1d=BRAW Page 1 2 3 4 5 e 7 8 g 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 45.5 45.7 46 47 48 49 50 51 52 53 HEAD,EXAM, 16,18.1,8,0,0, 1 , 4.60..60.. 0.,0., 6.,0.. 6.,3.. 0. .4. , 0, 1,0.,4..4,1, 2,0.,2..4,1, 3,0.,1.,4, 1, 5,2..3.7,5,0, 6,2.,2.,0,1, 8,2.,0.,0.1, 9.4. ,3.36,5,0, 10,4.,2.,0,1, 11.4.,1.,0,1, 13,6..3..4,1, 14,6.,2.,4,1, 15,6.,1.,4,1, 16,6.,0.,4,1, 1.1.1.0,1.6,5, 2,1,1,0,2,6,1, 3,1,1.0,2,7,6, 4,1,1,0.3,7,2, 5,1,1,0,3.8,7, 6,1,1.0.4,8,3, 7. 1,1,0,5,10.9, 8,1,1.0,6,10,5, 9,1,1.0,6.11,10, 10,1,1.0.7.11,6, 11,1.1,0,7,12.11. 12,1,1.0,8.12,7. 13,1,1.0,9,14,13, 14,1,1,0,10,14,9, 15,1,1,0,10,15,14, 16, 1 , 1 ,0, 1 1 , 15, 10, 17,1,1.0.11,16,15. 18,1,1.0,12,16.11. ROCK, 9.8.0.,0.. 5.0.5, 1 , 1,0..0.0001,1., 1,4., 2,4. , 3,4. , 4,4. , 5,3. , 6,3. . 7,3. , 8,3. , 100 L i s t i n g of WAND, a t 12:02:29 on JAN 30, 1985 f o r CC1d=BRAW Page 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 1 ^ E x e c u t i o n begins 6 MAXIT= 5 ********** Total Total Node 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 NODAL INFORMATION ********** number of nodes= 16 number of unknowns 3 Coordinates X Y 0.0 4.000 0.0 2.000 0.0 1.000 0.0 0.0 2.000 3.700 2.000 2.000 2.000 1.000 2.000 0.0 4.000 3.360 4.000 2.000 4.000 1.000 4.000 0.0 6.000 3.000 6.000 2.OOO 6.000 1.000 6.000 0.0 ********** 8 Known c o n d i t i o n 4 4 4 4 5 0 0 0 5 0 0 0 4 4 4 4 1 1 1 1 0 1 1 1 0 1 1 1 1 1 1 1 ELEMENT INFORMATION ********** T o t a l number of e l e m e n t 18 Maximum bandw1dth= 6 Number of q u a d r l l a t e r a l s = 0 Number of t n a n g l e s = 18 Element types: 1-Triangle 2-QuadMlateral 3 Element 1 2 3 4 5 6 .7 8 9 10 1 1 12 13 14 15 16 Material Type 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 Element Type 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 Movable c o n d i t i o n Nodes A s s o i a t e d with Element Code • 1 6 5 2 1 6 2 7 6 3 7 2 3 7 8 4 3 8 5 10 9 6 10 5 6 1 1 10 7 11 6 7 12 1 1 8 12 7 9 14 13 9 10 14 10 15 14 1 1 15 10 101 it Ing of WANO. a t 12:02:29 on JAN 30, 1985 f o r CC id=BRAW Page 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 1 10 11 1 112 113 1 14 1 15 1 16 117 118 1 1 17 18 1 1 **«*«*****Mater1al 1 1 16 12 16 15 11 propert1es********** U n i t weight of water************ 9.80 M a t e r i a l type Conductivity Conductivity Number in X d i r e c t i o n in Y direction 1 0.00010 0.00010 IT= 1 ************** + * * * * * p RATIO OF Ky/Kx IS 1.00000 0 u t DRAIN LENGTH 3 U t ^nformation ********* 0.0 (M) NODE NUMBER HYDRAULIC HEAD(m) WATER PRESSUI 1 4 .000 0 .0 4 .000 19 .600 2 3 4 .000 29 .400 4 4 .000 39 .200 5 3 .720 0 . 193 6 3 .695 16 .613 7 3 .688 26 .343 8 36 .121 3 .686 9 3 .392 0 .312 10 3 .366 13 .383 11 3 .357 23 .095 12 3 . 354 32 .868 13 3 .000 0 .0 14 3 .000 9 .800 15 3 .000 19 .600 16 29 .400 3 .000 Vx THIT ELEMENT Vy 1 0.000013801424 -0.000001439324 -5. 95373 2 0.000015240745 -0.0 0. 0 0.OOOO15240745 -O.OOO00O711495 -2. 67283 3 4 0.OOOO15596495 -0.0 0. 0 5 0.OOOO15596495 -0.000000222816 -0. 81848 6 0. 0 O.000015707890 -O.O 7 0.000016062913 -0.000001928770 -6. 84705 -4 .99172 8 0.000016478938 -0.000001439324 9 0.000016478923 -0.000000901329 -3 .13071 0.000016573846 •-0.000000711495 -2. 45812 10 11 0.000016573846 -0.000000273438 -0. 94519 12 0.000016599151 -0.000000222816 -0. 76905 0.OOOO19591855 -O.O O.O 13 14 0.000018280305 -0.000001928770 -6. 02302 15 0.000018280291 -0.0 0. 0 16 0.000017829632 -0.000000901329 -2. 89396 17 0.000017829632 -0.0 0. 0 18 0.000017692902 -0.000000273438 -0. 88541 *** UBC P l o t Subroutines - End of P l o t t i n g * * * Storage 0.0 102 Listing 119 120 121 122 123 124 125 126 of WAND, a t 12:02:29 o n JAN 30, 1985 f o r CC1d=BRAW Page 3 Number o f p l o t f r a m e s g e n e r a t e d = 1 I f t h i s p l o t 1s q u e u e d f o r p l o t t i n g 1t w i l l t a k e a p p r o x i m a t e l y 2 m i n u t e s t o p l o t a t an a p p r o x i m a t e c o s t of 0.11 d o l l a r s ( U n i v e r s i t y r a t e s ) and use 26 i n c h e s o f p a p e r . A p p r o x i m a t e l y 3 6 % o f t h e t i m e w i l l b e s p e n t p l o t t i n g w i t h the pen raised. * * * * * * * * * * C A L C U L A T I O N END ********** /^Execution t e r m i n a t e d
- Library Home /
- Search Collections /
- Open Collections /
- Browse Collections /
- UBC Theses and Dissertations /
- Numerical modeling of horizontal drain drainage in...
Open Collections
UBC Theses and Dissertations
Featured Collection
UBC Theses and Dissertations
Numerical modeling of horizontal drain drainage in an open pit slope Ge, Shemin 1985
pdf
Page Metadata
Item Metadata
Title | Numerical modeling of horizontal drain drainage in an open pit slope |
Creator |
Ge, Shemin |
Publisher | University of British Columbia |
Date Issued | 1985 |
Description | A study has been made to evaluate the effects of horizontal drain drainage on the water table drawdown in open pit slopes. Two major parameters of a horizontal drain drainage system, length and spacing, were studied. A two dimensional finite element computer model was constructed to simulate the water flow into drains in rock slopes. Water flow in the saturated zone was assumed. The computer model was tested by the field data obtained from the LORNEX Mine in British Columbia and the data taken from INTRODUCTION TO GROUNDWATER MODELING (Wang & Anderson, 1982). Satisfactory agreements were obtained. As the result of computer simulations, a series of graphs were plotted. These graphs show the relationship between hydraulic head distribution vs. drain spacing and length. They could be used in horizontal drain design as an aid to determine the spacing and length of a drain system. The computer simulations were also made to study the drainage characteristics of anisotropic rock slopes. The results indicated the influence of such rock conditions on the drainage effect. Another feature of mining slopes is that their height varies as the mining operation progresses. Therefore, the suitable vertical spacing between drain rows was investigated by computer simulation. A comparison of the drainage effects of different drain patterns, parallel drain and fanned drain layouts, was also made. |
Subject |
Drainage Slopes (Soil mechanics) |
Genre |
Thesis/Dissertation |
Type |
Text |
Language | eng |
Date Available | 2010-05-27 |
Provider | Vancouver : University of British Columbia Library |
Rights | For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use. |
DOI | 10.14288/1.0081165 |
URI | http://hdl.handle.net/2429/25096 |
Degree |
Master of Applied Science - MASc |
Program |
Mining Engineering |
Affiliation |
Applied Science, Faculty of Mining Engineering, Keevil Institute of |
Degree Grantor | University of British Columbia |
Campus |
UBCV |
Scholarly Level | Graduate |
Aggregated Source Repository | DSpace |
Download
- Media
- 831-UBC_1985_A7 G37.pdf [ 3.99MB ]
- Metadata
- JSON: 831-1.0081165.json
- JSON-LD: 831-1.0081165-ld.json
- RDF/XML (Pretty): 831-1.0081165-rdf.xml
- RDF/JSON: 831-1.0081165-rdf.json
- Turtle: 831-1.0081165-turtle.txt
- N-Triples: 831-1.0081165-rdf-ntriples.txt
- Original Record: 831-1.0081165-source.json
- Full Text
- 831-1.0081165-fulltext.txt
- Citation
- 831-1.0081165.ris
Full Text
Cite
Citation Scheme:
Usage Statistics
Share
Embed
Customize your widget with the following options, then copy and paste the code below into the HTML
of your page to embed this item in your website.
<div id="ubcOpenCollectionsWidgetDisplay">
<script id="ubcOpenCollectionsWidget"
src="{[{embed.src}]}"
data-item="{[{embed.item}]}"
data-collection="{[{embed.collection}]}"
data-metadata="{[{embed.showMetadata}]}"
data-width="{[{embed.width}]}"
async >
</script>
</div>
Our image viewer uses the IIIF 2.0 standard.
To load this item in other compatible viewers, use this url:
http://iiif.library.ubc.ca/presentation/dsp.831.1-0081165/manifest