Seepage_CSM8
Contents
1. 874 574 579 sz vel veel 583 584 585 585 see ser 588 588 583 589 53 53 53 532 533 533 533 534 534 534 534 535 535 535 sas 535 sss 535 596 sas 535 854 seel 558 vel 582 veel see ver ses 572 524 570 624 579 so 58 ses 584 ses 585 seel ser verl see 588 ses vas 53 53 sof 53 53 53 528 53 534 54 543 546 549 551 554 556 558 sei 583 565 ser seel 52 572 523 575 szef 621 528 579 Gel vol 582 583 583 584 584 585 ses 585 586 see 586 586 see sos soe ie 52 sos voel 631 5 35 Bas 542 sae vel 553 ssel 558 58 voe see see 57 571 524 575 szef 577 szef szol 579 sel sal sal sel sed 582 see es 485 3 496 el 505 51 siel sisl 523 521 531 sos 538 542 545 548 551 553 556 558 Ge 564 seel ser ses 67 szi s72 573 524 575 e 5 77 n 577 Lese 469 75 ser see soe s1 522 525 83 saf 538 544 sarf Ge 553 seel 559 581 563 564 566 seel ses sr 74 522 573 533 573 e a ER EER Ee eee ee EET od dis od ed ee a szef saal veel e deel ezel 4 79 sel 432 sel 503 sos sif sie 523 527 sa 535 538 541 44 ser 549 553 555 551 558 Ge vol seel ses 564 5642. ww AU m je je gt oo eo LY A s dm n n n m n n gt m TEL MIS gt gt fem Fer Ferm Va ji rm Jo Ja fe o j moo a gt je je fe fe fJ in um le Jo fin 2 de Fo Feo gt fe fe Ale el fio fio 2 jae ja Fo fe fe Fo m fin le e fio Ie gt gt fje gt Fo je fe fe io jo Jo le gt ar gt aki IE 2 ol eR 1 5 aa fo C val 13 13 13 12 12 12 1 4 1 4 2 12 13 4 13 EP EP EP H 14 Ge 3 Figure 7 Completed calculation of head distribution Contours of constant head can be interpolated from the results shown in Figure 7 For a contour spacing head drop of 0 5 m the equipotentials from the FDM spreadsheet can be compared to those drawn using the flow net sketching method outlined in the main text Figure 2 8 These are shown in Figure 8 from which it will be seen that both methods give an almost identical solution to the location of the equipotentials The flow lines could then be drawn in to give curvilinear squares if necessary however it 1s possible to determine the amount of seepage from the change in head along the discharge boundary without drawing flow lines Seepage 8
3. EE ME EE ME EE ME EE EE EE SE EE SE EE ME EE ME EE 20 10 10 5 Figure 3 Data entry The FD mesh may now be assembled As in the example from the main text the soil domain extends approximately 8 m either side of the sheet piling This requires 17 nodes at 0 5 m spacing from one edge of the soil domain up to and including the nodes along one side of the sheet piling As the pressures head along either side of the wall may be different nodes are required for both sides of the piling even though it has a negligible thickness A total of 34 nodes will therefore be required horizontally i e 34 columns 18 nodes are required vertically to model the 8 5 m depth of soil 1 e 18 rows The uppermost nodes representing the upper surface of the soil represent the recharge left hand side and discharge right hand side boundaries Values of head relative to the datum are known at these nodes and are entered in metres as shown in Figure 4 The left and right boundaries are then formed by copying the formulae for these boundary conditions from the FDM node library to the drawing area i e LB and RB respectively Note that of the 18 nodes required on this boundary the top node is on the discharge boundary value 0 5 m and the bottom node will be part of both the right boundary and the bottom boundary i e a bottom right corner BRC Only the 16 nodes in between should therefore have the RB 5 Seepage
4. 334 343 364 423 432 ner sasl 63 ezel azo seal ssl 495 e s 228 225 225 225 225 225 225 225 22e 22e 244 262 229 296 aze asf ar 389 3985 soel sil 420 34 442 45 ne seel 473 ezel sei nos seel sol ese 434 435 436 436 EM 44 sisse EEE MB eene ee er rd ed ed eed ed e e n Mi ML pe po pe Po pope pe poi po pei po pe pe pri pn sar eo EE EE eee li PP PP PP EE EIE EF BEER DE pepe pe prp EIS ES ESE 1 A us vas ves veel 203 224 24 251 224 23 soel sal 334 347 se 322 383 334 eo evo sai 425 435 443 449 asel 455 ses ser azal 475 477 ezel 473 02 025 oze zel oss 14 ve veel 182 22 23e 255 222 288 soo sil 4 345 ase seol sod as eod 41 427 ese e ser 452 sei ses ezel ee 477 477 os Lora vel vas ve vel vos 21 238 253 21 288 sif aal 343 356 see 374 sa 420 32 aof 445 ssil sel sel seal ner 42 szal ezel szef 476 025 028 os oss i 138 159 198 211 26 252 269 285 3 329 s42 aze 83 338 08 eve 24 3 38 44 45 455 459 seel 69 azi 23 szal ezel 475 025 oss ozzl oss wl 138 153 179 ese or 23 252 269 285 ol ave 323 342 ssal ses aze ssel 07 446
5. 8 User s Manual Flow net sketch Fig 2 8 main text spreadsheet E ya Figure 8 Comparison of FDM equipotentials with flow net sketch 6 The flow of pore water must become perpendicular to the discharge boundary as the fluid approaches the boundary Each set of vertical nodes in this region therefore represent flow lines The change in head Ah at the discharge boundary is therefore found at a given distance from the right edge of the wall as by entering the formula shown in Figure 9 This is then copied as shown Total head h m 05 05 05 m 0 7 5 05 oz ol oz il ali e os 03 os al al al EE ER Tu EE TT ENER ENER ETE ENER EE EE ET EP ET rr RPP EE EP EP te D EP EP EREM EE EE ER ET 5 gt 5 25 TELE EE ER ER EE Er EE Ee En Copied Figure 9 Calculation of flow rate Seepage 8 8 User s Manual The average amount of flow within the flow tube between each set of adjacent flow lines is then found by entering the formula shown in Figure 10 Total head h m 45 45 45 45 45 45 45 45 45 45 45 45 45 45 45 45 45 05 05 05 05 05 05 05 05 05 05 0 5 05 05 05 05 0 5 saf aal al aal saf ET ET ET ET EY sal ET ET aal ala FE FEET PE FESTER m Ol cal aah acl al 1444444 saf EEEEEEEREEE _ Bidet eee cM FEEEEEEEEEEEEEE ss es faa aad al of
6. a oe oel os osf os 1121414 58 131 13 13 12 12 1 7 sof ssf EP uf ul al al I 14 a va sahna 1 1 EE St 12 12 12 12 25 Ey EP En EV Er EVEN ES EV ETB FPES E a EREDNEEPEREPETEPEPETEPETEPETET 2 PRETENEEPETETETETEPETETETETETET 37 2 EREREEETETETETETETETEY 13 13 13 13 13 EE EE EE E E E EE EE 25 25 23 22 al 19 18 17 18 15 15 14 14 13 131 13 131 13 011 01 0 1 01 01 041 01 041 041 04 041 01 01 04 01 04 0 1 01 01 011 01 0 1 01 0 1 DA 04 01 0 1 0 1 01 0 1 sunicanze 8628 Figure 11 Calculation of flow rate contd 9 Seepage CSMS8 User s Manual Performing the calculations gives ZAA 1 4 The flow rate 4 can then be found as described in Section 2 7 Example 2 3 of the main text q k This gives q 1 4k which compares favourably to the value of q 1 5k found from the flow net sketch in Section 2 4 of the main text It can readily be seen by this example that use of the FDM in this way provides a very quick and simple way to determine total head and hence pore pressures if necessary and flow quantities for a seepage problem and is less subjective than the sketching of a flow net 4 APPLICATION TO WORKED EXAMPLES IN MAIN TEXT This section demonstrates how the FDM spreadsheet may be applied to the other worked examples included in Chapter 2
7. for nodes on the boundary of an impermeable element e g some sheet piling or the bottom of a foundation some of the adjacent cells will be inactive e g within the impermeable boundary As a result special versions of the basic node formula Equation 2 31 from the main text are required to correctly model the boundary conditions within the model The formulae employed are described in more detail in Section 5 of this manual The FDM node library section contains one example of each formula which may be copied into appropriate cells in the Drawing area see below to build up a complete FD mesh An example of this is provided in Section 3 The drawing area may be extended if necessary by inserting additional columns between columns BQ and BR and inserting additional rows after row 57 This may be necessary for problems in which a fine grid spacing is required to give a high level of detail in a large problem The Depth scale section auto calculates the depth in metres of each row of nodes using the grid spacing entered in Basic data The depth scale fixes zero at the level of the uppermost row of nodes used in the problem The uppermost row of nodes should therefore be entered in row 7 within the drawing area The examples in Section 4 include problems where soil levels may be unequal within the problem e g for an exacavtion for guidance This section also uses the input datum level to provide an alterantive scale which 1s the elevation hea
8. 23 Seepage 8 8 User s Manual Node Elevation above index Depth Datum z 0 0 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 66 6 6 6 6 6 6 6 6 6 6 6 6 6 6 1 0 25 5 75 o of of of of of o E 2 0 5 55 E E E o o 3 0 75 5 25 o of of of of of o 411 5 of op o ol of 5 125 4 75 of of of of of of o 6 15 45 E E E o 7 175 4 25 o of of of of of o 2 of of ol of of ol o 3 2 25 3 75 of of ol of of of of o o 10 25 35 of of ol ol of of of o TE 1 2 75 3 25 of of of of of o o o 20 op ol s of d of o ol 13 3 25 2 75 of of of of o of 14 35 25 15 3 75 2 25 16 4 2 17 4 25 1 75 18 45 15 19 4 75 125 20 5 1 21 5 25 0 75 22 5 5 0 5 23 55 025 Gol o o oj o o o o ol of o ol ol o ol ol o o ol o o ol oj o o ER E D EE T EE ER E DT MY EST D GT Y EP EST DT UT ET EE 2 24 6 0 Figure 25 Example 11 5b section 6 6 AE PRR AE EE EE EE se 55 55 55 55 sof 55 ssi 55 ssi 55668 s52 553 554 555 557 558 Gel 563 565 ser ses 524 575 szef 528 szal 529 58 58 583 583 583 583 583 EER ee re A rer prp ES EE ER ee Ee Fee Eos 5 el sol sol sol sol sol sol BOM sos 506 509 sel 5 52 525 53 534 538 5
9. 45 45 4 5 45 45 45 45 45 45 45 45 49105 51 5051 051 151 051095 95195 051 051 151 051 Dat 05 iE di Em jg o E yuo ia 0 dto Er gio En dio Bir alo te dio EE Lg yuo ie E dr gl Upper Right Pile URP ol m m _ el Intermediate Right Pile IRP Lig j i d a ay oj of ol ol ol of of ol od of of ol ol of of ol A of of ol ol of of ol ol of of ol of of of of of o Bottom Right Pile BRP Figure 5 Assembly of model contd 4 The remaining nodes in the interior of the soil body on either side of the wall are then filled using the generic INTERNAL CELL formula 1 as shown in Figure 6 Mode Elevation above index Depth Datum z 0 0 0 5 1 05 E 2 1 45 3 15 2 4 2 25 5 25 3 6 3 3 5 7 35 4 8 4 45 9 45 5 10 5 55 11 55 12 6 6 5 13 65 7 14 7 75 15 75 8 15 8 85 17 85 9 18 9 9 5 Total head h Seepage 8 8 User s Manual 4 5 45 4 51 45 45 45 45 45 45 45 45 do 45 45 45 45 45 05 0 51 05 Do 05 0 51 05 0 51 05 0 51 05 0 51 05 0 51 0 5 0 5 0 5 Figure 6 Assembly of model contd 5 Pressing F9 on the keyboard will then start the iterative calculation The numbers in the cells will initially change rapidly this change will slow down as the calculations converge to the solution shown in Figure 7 Once the calculation is complete the numbers in the cells represent the values of head at a particular point
10. 555 565 ER ER PEPERIT PSP OE pego ER EERS FEE FEES EIE 4 22 ses asal vol 33 s42 as sel ser 24 seil seel ssl 5 voe r sif G2 524 soe 532 525 sae sa 546 548 543 55 552 seed 55 ssel 556 557 551 552 227 as ssa aza 385 sor ave ezel 437 447 sel azi ezel 485 sel 503 508 sil 522 526 529 533 536 528 sai 543 548 Ge 55 552 553 553 553 553 as sool su sa os ssal ees aze esl ss sool sie 52 524 voel sai 524 527 539 541 543 548 546 542 548 543 55 55 ss 28 soe 338 349 aze ses 412 23 sol 443 52 sel ezel ssl ves 35 soi soel snf sil su 523 vor 531 533 535 539 541 543 544 545 sae 546 542 sel 375 seel 4 23 433 saal a52 sel seel ezel neo 89 asel 50 oe Gal 522 525 24 520 534 536 538 54 54 542 543 544 544 244 262 28 238 ve aal ses sod sisl 424 sas 44 62 477 84 ssl 436 sol soel Gul sre 519 522 525 528 531 533 535 sar 538 533 54 54 sel ass a 233 sel 379 2 sos 427 sarl asr 455 asal azal seo asr soo sel sis 522 525 528 53 s32 534 535 521 538 538 539 538 138 22 242 263 284 3031 sai asel 354 ses asa 336 sos 42
11. 8 8 User s Manual formula copied in The left boundary and bottom boundary BB can similarly be copied in as shown in Figure 4 Bottom Left Comer Bottom Right Corner BLO BRC Figure 4 Assembly of model 3 The nodes on either side of the sheet piling can similarly be incorporated using LB and RB nodes as shown in Figure 5 The nodes beneath the sheet piling are a special case as due to the small thickness of the sheet pile wall the nodes below each side of the sheet piling essentially represent the same point within the soil and so require special formulae to ensure that the heads calculated at these nodes will be consistent These formulae are given in the central column of the node library NODES AROUND amp BENEATH PILING The nodes at the toe of the wall i e at 6 m depth are represented by Upper Right Pile URP and Upper Left Pile ULP on the right and left sides of the wall respectively The nodes below this are modelled using the intermediate nodes IRP and ILP and those on the bottom boundary using the BRP and BLP nodes Further details on the formulation of these FDM nodes are given in Section 5 Node Elevation above index Depth Datum z 0 0 0 5 0 5 1 1 1 5 2 5 2 2 2 5 3 3 3 5 3 5 4 ON gt ho en 4 4 5 45 5 10 5 5 5 11 53 6 12 6 6 5 13 5 5 7 14 7 7 5 15 75 8 1 8 8 5 17 8 5 9 18 9 9 5 Total head Sheet piling indicative 45 45 45 45 45
12. al ol of of of oof oe oo os osf os osl PEFENENEEEFEEEEBE cal ch cal cal cl al a od aad ol coal cal cl call E EE EE HEE WE a EP EP EF s Ee Er ae Eed E 39 EB 38 sal cal sal aah sal sl ard ool aol ol oad eal acl cl oc E ph 38 32 sel 38 sel 37 32 37 sel ss 35 34 32 3 29 2 Ev EET Er EY EV ETEM ET ET ETER EE EN dad EE EE E TEE 041 D1 01 01 01 01j 04 DA OFT 04 01 DA 041 04 0 1 04 DA 127 27 Copied Figure 10 Calculation of flow rate contd Finally the change in head within all of the flow tubes is added together to give as shown in Figure 11 Once this last formula has been entered F9 must be pressed on the keyboard to perform all of the calculations entered during this step Total head h m 45 45 45 45 45 45 45 45 45 45 45 45 45 45 45 45 45 0 5 05 0 5 05 05 05 0 5 0 55 05 05 05 05 05 0 5 05 0 5 ES rs and 08 os os os os os os os os asl os os l a 3 OG oz 02 02 ozl oz 02 02 02 oz 02 02 os os os os 43 43 43 aal 42 42 42 42 2 2 42 2 42 42 quum mmm _ seien en edem enl col m oof vel ve os 08 os ET sa saf saf saf aal sal sa sal ol a al ah al ol eh al a 4 al a af os ET af aif aa EE EE EE EE EE EE ET ET eb s ul a
13. e how to model problems with layered soils Zero depth is set at ground level on the right hand side of the model and the datum is set at 6 m depth i e the water level in the excavation A grid spacing of m is used giving the FDM node layout shown in Figure 21 Note that the equivalent isotropic permeabilities of the upper and lower soil layers must be entered the kr and k cells respectively in the Basic Data section BEFORE 15 Seepage 8 8 User s Manual any calculation is attempted The current version of Flownet CSMS only supports two distinct soil layers 6 00m 8 00m HEIL H CU ER ER m C aus a 0000000900000 068 a 20000 HH 0 1 2 3 4 5 10 Figure 20 Example 2 3 section ld ey m m im le ww nnn Figure 21 FDM node allocation Example 2 3 16 Seepage CSMS User s Manual The resulting values of head may be found in the in the appropriate worksheet within Seepage CSMS xls The values of head may be extracted from the nodes representing the tunnel walls and the method described in the previous example may be used to convert these values into pore pressures The resulting pore pressure distribution is shown in Figure 22 100 80 60 40 20 40 60 80 100 100 80 60 40 20 0 Figure 22 Pore pressure dis
14. of the main text These are included as complete worksheets within Seepage CSMS xls Note that this implementation of the FDM is not suited to problems involving unconfined seepage e g flow through embankment dams As such only Examples 2 1 2 3 will be considered here These examples will demonstrate the use of the full range of nodal formulations included in the FDM node library including applications to sheet piling layered soils and buried Structures Example 2 1 Flow into a cofferdam The problem geometry is shown in Figure 12 This problem is similar to the worked example in Section 3 however it demonstrates e how to tackle problems with varying ground level e how to tackle problems involving symmetry e how to extract hydraulic gradient information from the FDM The soil domain is assumed to extend 8 m on either side of the excavation Zero depth is set at the level of the soil outside the excavation and the datum is set at 2 5 m depth 1 e the water level within the excavation A grid spacing of 0 5 m is used giving the FDM node layout shown in Figure 13 10 Seepage 8 8 User s Manual 5 50 m Sheet i 2 50 m piling Plane of _ Z symmetry 2 00 m Datum 6 00 m i 2 2bm 0 12 3 45 10m TT TT dt E Figure 12 Example 2 1 section 45 45 45 45 45 45 45 45 45 45 45 45 45 45 45 45 45 4 5 4 5 45 45 45 45 45 45 45 4 5 45 45 4 5 45 45 45 45 Figure 13 FDM node allocation Example
15. 2 1 The resulting head distribution within the model may be found in the appropriate worksheet within Seepage CSMS xls It will be seen that the solution is symmetric and validates the symmetry assumptions made in the main text when sketching the flow net A half FDM model could equally well have been used which would have given the same solution Equipotentials have been derived from head distribution and are compared with those obtained from the flow net sketch in the main text in Figure 14 11 Seepage CSMS8 User s Manual Flow net sketch _7 AS Figure 14 Comparison of FDM left and flow net sketch right FDM XK ya m gt mm lt 7 wu v s p 4 7 1 d MEE The hydraulic gradient immediately below the excavated surface is found using the change in head between the nodes just below the surface and the discharge boundary towards the centre of the excavation This can be determined as in Section 3 giving Ah 0 26 m This drop in head occurs between two adjacent nodes which are 0 5 m apart grid spacing so As 0 5 m Therefore i Ah As 0 52 which compares favourably with the value of 0 5 derived from the flow net sketch in the main text Example 2 2 seepage beneath a dam spillway The problem geometry is shown in Figure 15 This problem demonstrates e how to incorporate an impe
16. 24 444 eel 455 453 463 seel 473 475 475 Figure 26 Example 11 5b contd 24
17. 42 sae 548 551 553 558 558 553 sei 562 564 ser nos 566 ser ser ser se Mid eee ee ee eee ee mi uico Mum le al e lal a ula u 425 425 ae 420 zel 425 42e sze 28 sze 21 427 ezel 429 43 422 ese sel sel seel sol sif sel 52 525 528 534 536 538 54 sai sel 543 544 544 saa Eos af sol sol so sol sod sol dol 4 024 s02 soz 02 soal ooh 4 25 sai 454 azal sol seo 95 sol sos sr sil sis 522 525 528 53 s32 533 sos sae 526 53 Lage 325 37e 276 szef aze zel aze szef asl en ezel saf ee err oe 3 sel 502 sos saf sr 52 522 524 526 521 523 24 53 53 29 38 sel sel sel 351 see 383 333 eve 427 439 49 ar azal aar 433 sarf sool soe sos 512 sis sv sis 52 522 523 523 523 aas 224 225 24 sa sel 224 sel azo so C7 EP asel sasl sool vae sasl aas vee 474 474 voe ses sof ese soo or ERIT EP EP sel rl EF 43 arr 333 349 ses sel ass 06 29 saol 448 56 azel sez aar sel 433 502 soe soe 508 sos 81 su Lage 275 274 275 275 225 215 225 215 275 276 253 sos ozel 85 398 1 42 3 sel ssel ssel 63 469 475 eel 85 seol 36 ssel 8 sool soe soe 505 soe 25 25 25 25 25 oes 286
18. Left Pile zs h ILP Bottom Left Pile BLP Upper Right Pile URP Intermediate Right Pile z h IRP A Bottom Right Pile BRP 19 Seepage 8 8 User s Manual Node type Governing equation Representation in node library Bottom Right Re entrant BRR Bottom Left Re entrant BLR Upper Left Re entrant ULR Upper Right Re entrant URR h h 2h 2h h 6 h 2h 2h h h h 6 Ah h h 2hy i 6 h h h 2h 2h i 6 20 Seepage 8 8 User s Manual Representation in node h gt nternal cell h Ah h Ah Layered p ovo IL Right Boundary Ah 2h As ha Layered 4 RBL Left Boundary 2h Layered 4 LBL Upper Left hy Es 5 h A Pile Layered N Fe 2 3 4214 ULPL Upper Right Pile Layered URPL Intermediate Left Pile hy A hy h Aha Layered T 4 ILPL h Intermediate Right Pile h Ah h Ash pa 12 3 24 Layered 4 IRPL C kk 2 ktk 21 Seepage 8 8 User s Manual APPENDIX This appendix demonstrates the use of Seepage CSMS xls for analysing the drained backfill in the retaining wall problem of Example 11 5 This problem demonstrates e how to incorporate a linear drain within models e how to determine the resultant pore water pressure thrust on a plane within the soil for use in the Coulomb wedge m
19. Seepage_CSM8 A spreadsheet tool implementing the Finite Difference Method FDM for the solution of two dimensional steady state seepage problems USER S MANUAL J A Knappett 2012 This user s manual and its associated spreadsheet Flownet_CSM8 xls accompanies Craig s Soil Mechnics 8 Edition J A Knappett amp Craig The spreadsheet Flownet CSM8 is an implementation of the methodology outlined in Williams B P Smyrell A G and Lewis P J 1993 Flownet diagrams the use of finite differences and a spreadsheet to determine potential heads Ground Engineering 25 5 32 8 Seepage CSMS8 User s Manual 1 INTRODUCTION This manual will explain how to use the spreadsheet analysis tool Seepage CSMS xls to solve a wide range of two dimensional steady state seepage problems This spreadsheet is an implementation of the Finite Difference Method FDM described in Section 2 7 of the main text Spreadsheets offer a number of advantages for solving such problems namely e The tabular layout is particularly suited for forming a two dimensional mesh in which each cell represents a node of the mesh The problem as laid out on screen will therefore bear a strong visual resemblance to the problem being addressed e As the total head at each node depends on the values of the nodes around it it is required to solve a large number of simultaneous equations This can be done effectively and efficiently using the
20. The distance along the slip plane from one orange cell to the next is found by Pythagoras Theorem one cell across 0 25 m two up 0 5 m so AL 0 56 m The values of h and z can then be extracted for each orange cell the pore water pressure at each point is then found using Equation 2 1 These values are then numerically integrated along the slip plane using the trapezium rule to give U 36 8 kN m per metre length Example 11 5 b sloping drain behind retaining wall The sloping drain in Example 11 5 b is modelled in the same way except that the cells representing the drain now fall on a 45 line as shown in Figure 25 The left hand boundary is now impermeable representing the back of the concrete retaining wall starting from the bottom left hand corner the internal cells within the mesh are replaced with the value of elevation head in each row The calculation then proceeds as normal by pressing F9 The resultant pore water thrust is to be found along the same plane as before Starting from the bottom left hand corner a point close to the failure plane is found by going up two cells for every one across These cells are highlighted in dark orange in Figure 26 The values of hand z can then be extracted for each orange cell the pore water pressure at each point is then found using Equation 2 1 These values are then numerically integrated along the slip plane using the trapezium rule to give U 0 43 kN m 0 per metre length
21. d z above the datum Note that positive values of z indicate nodes which are above the datum As the elevation head is the same for all nodes within a row the worksheet provides the user with both values of h by calculation see Section 3 and z at all nodes within the model The distribution of 3 Seepage CSMS8 User s Manual pore pressure within the model can therefore be obtained by application of Equation 2 1 from the main text at each node This may be efficiently conducted for a given problem using the remaining cells in the worksheet as necessary The workbook Seepage CSMS xls contains a series of worksheets which are named as shown below New analysis Example 2 1 Example 2 2 Example 2 3 Example 2 5 Lw Lb 0 Example 2 5 Lw 9 1 Example 2 5 Lb 9 1 Example 11 5a Example 11 5b Each of these worksheets has the structure described previously though in all cases except New analysis a completed solution is presented the New analysis sheet having been used in each case to analyse a worked example from the main text The use of the New analysis sheet to solve a seepage problem will be described in Section 3 of this manual the remaining sheets will be discussed in Section 4 2 3 WORKED EXAMPLE To illustrate how the FD mesh is assembled and analysed this section will consider the example presented in Section 2 4 of the main text which was used to describe the flow net sketching techn
22. delling of drains within a body of soil with reference to the backfilled retaining wall problem in Example 11 5 2 PROGRAMME DESCRIPTION The spreadsheet analysis tool essentially consists of a single worksheet in which all calculations are conducted and which contains all of the necessary information for solving a problem by the FDM The worksheet consists of four sections as shown schematically in Figure 1 Seepage CSMS8 User s Manual FDM node Drawing area ER GEN m Depth scale Figure 1 Worksheet structure The Basic data section contains cells for user input data including the spacing between nodes a square grid with uniform spacing in both horizontal and vertical spacing is implemented in the current version of the software the depth at which the datum for head measurement has been selected and cells for inputting permeability if layered soils are to be modelled with different isotropic permeabilities k ko Note that for problems in which only a single layer of soil is present the head distribution 1s independent of the permeability of the soil and the permeability cells may be left blank The spreadsheet may also be used to analyse problems with anisotropic soils by using equivalent isotropic permeabilities K K Below the Basic data section is the FDM node library As the formulation of the basic equation governing the head at any node depends on the cells around it
23. ethod of analysis Section 11 5 Only the retained soil is modelled in this case assuming that the underlying soil is relatively impermeable Zero depth is set at the top of the retained soil and the datum is set at 6 m depth i e the bottom of the retained soil The head along the top surface of the soil is therefore 6 m pore pressure 0 elevation 2 6 m A grid spacing of 0 25 m is used Example 11 5 a vertical drain behind retaining wall The upper right hand side and bottom boundaries are set as before The drain is vertical and runs along the back of the retaining wall Within the drain the pore pressure must always be zero so the head will always be equal to the elevation head 1 e is independent of the adjacent cells This can be modelled by setting each of the cells on the left hand boundary equal to the value of elevation in that row giving the FDM node layout shown in Figure 23 2 e m E ho Figure 3 Example 11 5a section The calculation then proceeds as normal by pressing F9 For the Coulomb wedge analysis the resultant pore water thrust along a plane inclined at 6 45 0 2 64 to the horizontal is to be found Starting from the bottom left hand corner a point close to the failure plane is found by going up two cells for every one across These cells are highlighted in dark orange in Figure 24 22 Seepage 8 8 User s Manual 6 6 6
24. he underside of the spillway may be copied out The elevation head z from column Z for each node may then be used to determine the uplift pressures acting on the spillway using Equation 2 1 from the main text u y h z This method may similarly be applied for the nodes along either side of the sheet piling to determine the net pore pressures acting on the piling Note that this is the same method used in the main text however the FDM is particularly suitable for this application as the heads are automatically determined at the same points along each side of the wall The uplift pressure distribution on the underside of the spillway and the net pore pressures on the sheet piling are compared with those determined from the flow net sketch main text in Figures 18 and 19 respectively Seepage CSMS User s Manual Distance from downstream end m 0 5 10 15 0 9 Flownet sketch O Finite Difference O o Uplift pressure kN m 40 50 60 Figure 18 Comparison of uplift pressures on spillway Net fluid pressure kN m 0 10 20 30 2 3 e 9 Flownet sketch 4 O Finite Difference gt D 5 6 Figure 19 Comparison of net pore fluid pressures on sheet piling Example 2 3 Excavation next to buried tunnel in layered soil The problem geometry is shown in Figure 20 This problem demonstrates e how to incorporate an impermeable structural element which is completely buried
25. igue The example is shown in Figure 2 The steps required to solve the problem are illustrated below 0 1 2 3 4 5 10m Figure 2 Example problem section 4 Seepage 8 8 User s Manual 1 For this problem a grid spacing of 0 5 m is selected This means that almost all of the dimensions in Figure 2 can be represented exactly by whole numbers of nodes The depth of 8 6 m between the soil surface and the lower impermeable layer will here be approximated as 8 5 m which is expected to have a negligible influence on the resulting seepage The value of 0 5 is entered into the grid spacing cell in the Basic data section as shown in Figure 3 As in the main text the datum will be selected at 0 5 m depth i e the downstream water level The spreadsheet is programmed to calculate the results of formulae only when requested by the user After entering the grid spacing and datum level pressing F9 will calculate the depth scale and elevation heads in the Depth scale section Depth scale Node Elevation above index Depth Datum z Total head h m BOUNDARIES BETWEEN SOIL LAYERS EE mE EEN P givin CO A ho ha ei vo EE gt ao U N O co e ea LR co 4 e Un n Midi 2 wo A e BOTTOM SURFACE gt Lm e b mm mm mm mm ME
26. iterative calculation techniques embedded within modern spreadsheets e Spreadsheet software is a standard component of most suites of office applications which are installed as standard on most computers e g Microsoft Excel within the Microsoft Office suite or Calc within the Open Office suite They are therefore almost universally accessible to students and practicing engineers without the need to buy additional expensive software This manual is structured as follows Section 2 Section 3 Section 4 Section 5 Appendix The basic structure of both the workbook Seepage CSMS xls and the worksheet used to perform the analyses will be described and the principle of operation will be highlighted This section will describe step by step how to use the basic worksheet to analyse a new seepage problem The resulting values of head will be used to derive equipotentials which will be compared to those obtained using a flow net sketch The spreadsheet tool has further been used to analyse other worked examples from the main text These are compared with the solutions obtained by flow net sketching to validate the method These examples demonstrate how different types of boundary conditions e g structural elements soil layering may be implemented within models This section describes the library of different FDM nodes implemented within the spreadsheet tool and provides further detail of the governing equations Describes the mo
27. rmeable structural element which is partially buried e how to model structures with combined horizontal boundaries and sheet piling e how to derive pore pressure distributions on structural elements The soil domain is assumed to extend approximately 5 m on either side of the spillway Zero depth is set at ground level not foundation level and the datum is set at depth i e the downstream water level A grid spacing of 0 7 m is used giving the FDM node layout shown in Figure 16 12 Seepage 8 8 User s Manual 15 20 10 012345 Figure 15 Example 2 2 section ea aa eaa eaa eaa a aa ea aa e a eaa 2 aa ea eaa eaa aa eaa aa ea eaa a eaa aa Figure 16 FDM node allocation Example 2 2 The resulting values of head may be found in the in the appropriate worksheet within Seepage CSMS xls The equipotentials derived from the FDM calculations are compared with the 2 5x10 m s see main text 3 7x10 m s per m length This compares favourably with the value of 3 75x10 m s per m length determined from the flow net sketch flow net sketched in the main text in Figure 17 The flow rate of water seeping underneath the spillway is found using the method described in Section 3 gt 1 48 m and so that q 13 Seepage CSMS8 User s Manual Figure 17 Comparison of FDM dashed lines and flow net sketch solid lines The values of head at the nodes along t
28. sel sel ser 24 sei verl 33 sel sos soel sie is 523 525 528 53 532 533 534 535 sae 536 247 263 23 309 328 345 sel aze seol si ss 35 sasl 54 477 nen ssl soel Gl sif sel 52 523 525 szef 53 azl 533 534 836 626 183 18 207 233 256 228 239 31 336 353 368 383 336 09 aal 4 ssl 459 sex ezel sei 493 ese 503 Gu sil sa 24 soel 528 529 532 532 533 53 132 29 245 268 29 329 363 az 31 404 sif 427 sar sar ssel asel ezel 485 ss sel sol soe 509 5 5 siel is 522 524 528 528 sos 53 532 522 inf ese uzel 208 235 28 283 304 24 342 358 323 soi sisl 424 435 ssl ssal 51 aze 83 sel 434 39 soe 542 sil su sal 523 525 21 soel sos 53 sal ase ver 193 228 254 2 3 ane 34 385 seel anl 24 33 se see ere sei sol sel sel 52 522 524 529 5 27 529 523 sal 53 Loze 124 ve 193 223 25 275 291 sel 336 353 33 ser nsl 2 sai ed eel sol sex 424 sei ese sor soo soel 51 is 522 524 528 522 528 529 523 529 oer wel 152 222 243 273 236 316 335 352 seel 383 sel ns 42 sel es esl 466 24 sel 486 sorl sool soel 51 sio sis soo 524 525 521 528 523 523 529 Figure 24 Example 11 5 contd
29. tribution around tunnel all values in kPa The flow rate is found as in the previous example by considering the change of head Ah just below the level of the excavation From the spreadsheet this is found to be XAA 3 30 At this level the water is flowing through soil 1 with permeability so This gives g 3 3x10 m s per m length 5 NODE LIBRARY This section describes the different nodal formulae which are available within Seepage _CSM8 xls and provides the theoretical formulation of each These are split into four separate tables over pages 18 21 inclusive p 18 Basic nodes for modelling impermeable boundaries and general soil nodes p 19 Nodes for modelling soil beneath thin impermeable elements e g sheet piling p 20 Nodes at the corner of an impermeable buried structure p 21 Advanced nodes for modelling horizontal soil layer boundaries where there is a change in permeability 17 Seepage CSMS8 User s Manual Node type Governing equation Representation in node library Upper Left Corner ULC Upper Boundary UB Upper Right Corner URC Right Boundary RB Bottom Right Corner BRC Bottom Boundary BB Bottom Left Corner BLC Left Boundary N 2h h h LB 7 4 Internal Cells N h h h h I 4 18 Seepage 8 8 User s Manual Node type Governing equation Representation in node library Upper Left Pile ULP Intermediate
30. within the soil continuum Node Elevation above index Depth Datum z 0 0 0 5 1 0 5 1 2 1 1 5 3 1 5 2 4 2 2 5 5 2 5 3 3 3 5 3 5 4 8 4 4 5 8 45 5 10 5 55 11 5 9 B 12 B 6 5 13 6 5 7 14 7 7 5 15 73 8 1 8 8 5 17 8 5 9 18 9 95 Total head h m 4 5 45 45 45 45 do 45 45 45 45 45 do 45 45 45 45 45 Oo 05 05 05 05 0 51 05 0 51 05 0 5 05 05 05 05 0 5 aal 43 aal 43 43 43 aal 43 aal as Pep e e e ER ER ER ER es ss ET ET ET ET onl ol os o os s s s os ED ER os ER ER ET ET al 44 43 oz 02 02 02 oz 02 oz 02 02 06 os os TE FEE PIT FT EE EE FEE EEE EE EE RE apos Loa osf osl oal osl azl azl ol PEER se al so arl ast 32 sel sel 35 a sal se s 35 34 8 sel sel sel s 35 sal 33 32 as sel sel 32 37 EER ET ET Er ET EMET ETE Er ET EEE j A io io m w co co js jw Jin co co Co Co eo in P gt co Co Foo Co gt gt m f o o fio fio je w co Joo gt jip m ja o o Je io co co gt ip m jm jo o co o o o
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