Companion program to Geotechnical Engineering: Principles and Practiced, Second Edition Coduto, Yeung, & Kitch (2011)
Finite difference solution for flow under sheet pile.
Soultion to example shown in Figure 8.4, Pg 305
Setup
If you opend this file and received an error message about circular references, you need to set spreadsheet to allow iterative computations.
Computations Tab
All the calcuations are done on the computations tab
<- Blue cells are equipotential boundaried
<-Orange cells are flow boundaries
<-White cells are non-boudary cells
<- Blue cells are equipotential boundaried
<-Orange cells are flow boundaries
<-White cells are non-boudary cells
<-Value of upstream head
To perform calculations, enter the upstream head value in the red cell and hit F9
The matrix below is the solution to the potenal function
10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 9.804490.192930000000000000000000000000000000
9.93113 9.93091 9.93023 9.92909 9.92748 9.92539 9.92281 9.91972 9.91609 9.91191 9.90714 9.90175 9.8957 9.88896 9.88149 9.87324 9.86416 9.8542 9.84333 9.83151 9.81872 9.80496 9.79027 9.77475 9.75857 9.742 9.72539 9.70914 9.6934 9.67723 9.65568 9.60899 0.38587 0.33977 0.31841 0.30233 0.28663 0.2704 0.25382 0.23726 0.22109 0.20559 0.19091 0.17715 0.16437 0.15255 0.14169 0.13174 0.12266 0.11441 0.10694 0.10021 0.09417 0.08878 0.08401 0.07983 0.0762 0.07311 0.07052 0.06844 0.06683 0.06569 0.06501 0.06478
9.86274 9.8623 9.86094 9.85867 9.85547 9.85131 9.84616 9.83999 9.83277 9.82442 9.81491 9.80417 9.79212 9.77869 9.76379 9.74733 9.72921 9.70934 9.68764 9.66402 9.63843 9.61086 9.58139 9.55018 9.51756 9.48405 9.45045 9.41779 9.38724 9.35989 9.33651 9.32014 0.67103 0.65482 0.63157 0.6043 0.57381 0.54119 0.50762 0.47415 0.44155 0.41036 0.38091 0.35336 0.32778 0.30418 0.28248 0.26262 0.24452 0.22806 0.21317 0.19974 0.1877 0.17696 0.16745 0.15911 0.15188 0.14572 0.14057 0.13641 0.1332 0.13093 0.12957 0.12913
9.7953 9.79464 9.79262 9.78923 9.78445 9.77825 9.77057 9.76137 9.75059 9.73815 9.72397 9.70794 9.68996 9.66992 9.64768 9.62311 9.59605 9.56636 9.5339 9.49853 9.46015 9.41872 9.37429 9.32706 9.27746 9.22625 9.17461 9.12435 9.07794 9.03859 9.01036 8.99859 0.98866 0.97694 0.94878 0.90951 0.86316 0.81295 0.76137 0.71019 0.66063 0.61343 0.56903 0.52762 0.48926 0.45391 0.42146 0.39179 0.36475 0.34018 0.31795 0.29792 0.27995 0.26393 0.24975 0.23731 0.22653 0.21733 0.20966 0.20345 0.19867 0.19528 0.19326 0.19259
9.72927 9.72839 9.72572 9.72124 9.71492 9.70671 9.69656 9.6844 9.67014 9.65368 9.63492 9.61371 9.58993 9.56341 9.53397 9.50143 9.46558 9.42622 9.38312 9.3361 9.28497 9.22963 9.17004 9.10637 9.03904 8.96891 8.89746 8.82712 8.76162 8.70625 8.6678 8.65352 1.32979 1.31555 1.27716 1.22185 1.15641 1.08614 1.01475 0.94466 0.87738 0.81375 0.7542 0.69888 0.64778 0.60078 0.55771 0.51837 0.48253 0.45001 0.42058 0.39407 0.37029 0.3491 0.33034 0.31389 0.29963 0.28747 0.27732 0.26911 0.26278 0.2583 0.25563 0.25475
9.66509 9.66401 9.66071 9.65517 9.64735 9.63719 9.62464 9.60959 9.59195 9.57159 9.54837 9.52214 9.49271 9.45988 9.42343 9.38313 9.33869 9.28986 9.23634 9.17785 9.11409 9.04484 8.96994 8.88941 8.80349 8.71294 8.61924 8.52513 8.43525 8.35703 8.30113 8.27995 1.69952 1.67835 1.62251 1.54436 1.45456 1.36051 1.26688 1.17639 1.09053 1.01004 0.93519 0.86598 0.80225 0.74378 0.69029 0.64148 0.59707 0.55678 0.52035 0.48753 0.45811 0.43188 0.40868 0.38832 0.37068 0.35564 0.34308 0.33293 0.3251 0.31956 0.31625 0.31516
10 9.84977 9.71144 9.57221 9.42958 9.28259 9.1304 8.97209 8.80666 8.63302 8.45004 8.25648 8.05107 7.83243 7.59914 7.34965 7.08236 6.79559 6.48757 6.15649 5.8005 5.41778 5.0066 4.56541 4.09303 3.58882 3.05296 2.48675 1.89296 1.2761 0.64248 0 0 0.64248 1.2761 1.89296 2.48675 3.05296 3.58882 4.09303 4.56541 5.0066 5.41778 5.8005 6.15649 6.48757 6.79559 7.08236 7.34965 7.59914 7.83243 8.05107 8.25648 8.45004 8.63302 8.80666 8.97209 9.1304 9.28259 9.42958 9.57221 9.71144 9.84977 10
10 9.85761 9.71824 9.57857 9.43644 9.29049 9.13962 8.9828 8.81898 8.64707 8.46591 8.27429 8.07092 7.85445 7.62344 7.37636 7.11161 6.82747 6.52217 6.19384 5.84057 5.46042 5.05151 4.61206 4.14057 3.63602 3.09812 2.52771 1.92716 1.30088 0.65555 0 0 0.65555 1.30088 1.92716 2.52771 3.09812 3.63602 4.14057 4.61205 5.05151 5.46042 5.84057 6.19384 6.52217 6.82747 7.11161 7.37636 7.62344 7.85445 8.07092 8.27429 8.46591 8.64707 8.81898 8.9828 9.13962 9.29049 9.43644 9.57857 9.71824 9.85761 10
10 9.86244 9.72534 9.58739 9.44713 9.3033 9.15478 9.00051 8.8394 8.67036 8.49224 8.30384 8.10388 7.89101 7.66381 7.42076 7.16023 6.88052 6.57979 6.25613 5.90751 5.53183 5.12695 4.69073 4.22118 3.71657 3.1758 2.59879 1.98709 1.34472 0.67883 0 0 0.67883 1.34472 1.98709 2.59879 3.1758 3.71657 4.22117 4.69073 5.12695 5.53183 5.90751 6.25613 6.57979 6.88052 7.16023 7.42076 7.66381 7.89101 8.10388 8.30384 8.49224 8.67036 8.8394 9.00051 9.15478 9.3033 9.44713 9.58739 9.72534 9.86244 10
10 9.86682 9.73329 9.59851 9.46138 9.32081 9.17571 9.02505 8.86775 8.70273 8.52886 8.34495 8.14974 7.94191 7.72004 7.48263 7.22805 6.95458 6.66035 6.34338 6.00152 5.63245 5.23373 4.80275 4.33682 3.83328 3.28974 2.70456 2.07771 1.41206 0.71507 0 0 0.71507 1.41206 2.07771 2.70456 3.28973 3.83328 4.33682 4.80275 5.23373 5.63245 6.00152 6.34338 6.66035 6.95458 7.22805 7.48263 7.72004 7.94191 8.14974 8.34495 8.52886 8.70273 8.86775 9.02505 9.17571 9.32081 9.46138 9.59851 9.73329 9.86682 10
10 9.87156 9.74248 9.61197 9.47908 9.34283 9.20221 9.05622 8.90382 8.74395 8.57552 8.39735 8.20822 8.00684 7.79182 7.56166 7.31476 7.04939 6.76366 6.45553 6.12272 5.76273 5.37277 4.94973 4.49009 3.98999 3.4453 2.85199 2.20712 1.51075 0.76937 0 0 0.76937 1.51075 2.20712 2.85199 3.4453 3.98999 4.49009 4.94972 5.37277 5.76273 6.12272 6.45553 6.76366 7.04939 7.31476 7.56166 7.79182 8.00684 8.20822 8.39735 8.57552 8.74395 8.90382 9.05622 9.20221 9.34283 9.47909 9.61197 9.74248 9.87156 10
Sheet Pile Wall
The matrix below is the conjugate to the above matrix and is the solution to the flow function
Equipotential Lines
Flow Lines